LMFDB - Embedded newform 378.2.v.a.193.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.6
Character	$\chi$	$=$	378.193
Dual form			378.2.v.a.331.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(-0.289127 + 1.70775i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.25076 - 0.819210i) q^{5} +(1.73201 - 0.0118132i) q^{6} +(2.25488 - 1.38402i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.83281 - 0.987512i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.289127 + 1.70775i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.25076 - 0.819210i) q^{5} +(1.73201 - 0.0118132i) q^{6} +(2.25488 - 1.38402i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.83281 - 0.987512i) q^{9} +(-1.19760 - 2.07431i) q^{10} +(-0.742338 - 0.270189i) q^{11} +(-0.312394 - 1.70365i) q^{12} +(0.651399 - 0.237090i) q^{13} +(-1.75455 - 1.98029i) q^{14} +(0.748249 + 4.08059i) q^{15} +(0.766044 - 0.642788i) q^{16} +(4.10222 + 7.10526i) q^{17} +(-0.480597 + 2.96125i) q^{18} +(2.46823 - 4.27510i) q^{19} +(-1.83484 + 1.53961i) q^{20} +(1.71161 + 4.25093i) q^{21} +(-0.137179 + 0.777978i) q^{22} +(0.428299 - 2.42900i) q^{23} +(-1.62352 + 0.603483i) q^{24} +(0.564595 - 0.473751i) q^{25} +(-0.346602 - 0.600332i) q^{26} +(2.50546 - 4.55221i) q^{27} +(-1.64553 + 2.07177i) q^{28} +(3.76826 + 1.37153i) q^{29} +(3.88866 - 1.44547i) q^{30} +(5.43257 - 1.97729i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(0.676045 - 1.18961i) q^{33} +(6.28497 - 5.27372i) q^{34} +(3.94139 - 4.96232i) q^{35} +(2.99972 - 0.0409212i) q^{36} +1.88252 q^{37} +(-4.63876 - 1.68837i) q^{38} +(0.216553 + 1.18097i) q^{39} +(1.83484 + 1.53961i) q^{40} +(-11.7991 + 4.29451i) q^{41} +(3.88913 - 2.42377i) q^{42} +(0.552932 + 3.13583i) q^{43} +0.789980 q^{44} +(-7.18496 + 0.0980148i) q^{45} -2.46647 q^{46} +(-1.47259 - 0.535978i) q^{47} +(0.876236 + 1.49406i) q^{48} +(3.16898 - 6.24160i) q^{49} +(-0.564595 - 0.473751i) q^{50} +(-13.3201 + 4.95125i) q^{51} +(-0.531025 + 0.445583i) q^{52} +(-4.62037 + 8.00272i) q^{53} +(-4.91812 - 1.67692i) q^{54} -1.89217 q^{55} +(2.32604 + 1.26077i) q^{56} +(6.58717 + 5.45117i) q^{57} +(0.696346 - 3.94917i) q^{58} +(-9.91385 - 8.31871i) q^{59} +(-2.09877 - 3.57858i) q^{60} +(2.49273 + 0.907280i) q^{61} +(-2.89061 - 5.00668i) q^{62} +(-7.75439 + 1.69395i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.27192 - 1.06726i) q^{65} +(-1.28893 - 0.459201i) q^{66} +(0.213835 - 1.21272i) q^{67} +(-6.28497 - 5.27372i) q^{68} +(4.02429 + 1.43372i) q^{69} +(-5.57134 - 3.01982i) q^{70} +(-3.32517 + 5.75936i) q^{71} +(-0.561196 - 2.94704i) q^{72} -7.17241 q^{73} +(-0.326897 - 1.85392i) q^{74} +(0.645809 + 1.10116i) q^{75} +(-0.857208 + 4.86147i) q^{76} +(-2.04783 + 0.418167i) q^{77} +(1.12543 - 0.418337i) q^{78} +(-1.70323 - 9.65951i) q^{79} +(1.19760 - 2.07431i) q^{80} +(7.04964 + 5.59487i) q^{81} +(6.27815 + 10.8741i) q^{82} +(-5.17113 - 1.88214i) q^{83} +(-3.06229 - 3.40916i) q^{84} +(15.0538 + 12.6317i) q^{85} +(2.99218 - 1.08906i) q^{86} +(-3.43174 + 6.03869i) q^{87} +(-0.137179 - 0.777978i) q^{88} +(-1.28793 + 2.23076i) q^{89} +(1.34418 + 7.05878i) q^{90} +(1.14069 - 1.43616i) q^{91} +(0.428299 + 2.42900i) q^{92} +(1.80602 + 9.84915i) q^{93} +(-0.272123 + 1.54329i) q^{94} +(2.05319 - 11.6442i) q^{95} +(1.31920 - 1.12236i) q^{96} +(-2.83825 - 16.0965i) q^{97} +(-6.69706 - 2.03699i) q^{98} +(1.83609 + 1.49846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	−0.289127	+	1.70775i	−0.166927	+	0.985969i
$3$	−0.289127	+	1.70775i	−0.166927	+	0.985969i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	2.25076	−	0.819210i	1.00657	−	0.366362i	0.214456	−	0.976734i	$-0.431202\pi$
$5$	2.25076	−	0.819210i	1.00657	−	0.366362i	0.792115	+	0.610372i	$0.208980\pi$
$6$	1.73201	−	0.0118132i	0.707090	−	0.00482272i
$7$	2.25488	−	1.38402i	0.852265	−	0.523110i
$7$	2.25488	−	1.38402i	0.852265	−	0.523110i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−2.83281	−	0.987512i	−0.944270	−	0.329171i
$10$	−1.19760	−	2.07431i	−0.378716	−	0.655955i
$11$	−0.742338	−	0.270189i	−0.223823	−	0.0814651i	0.227674	−	0.973737i	$-0.426888\pi$
$11$	−0.742338	−	0.270189i	−0.223823	−	0.0814651i	−0.451498	+	0.892272i	$0.649110\pi$
$12$	−0.312394	−	1.70365i	−0.0901804	−	0.491800i
$13$	0.651399	−	0.237090i	0.180665	−	0.0657568i	−0.250103	−	0.968219i	$-0.580465\pi$
$13$	0.651399	−	0.237090i	0.180665	−	0.0657568i	0.430769	+	0.902462i	$0.358242\pi$
$14$	−1.75455	−	1.98029i	−0.468923	−	0.529255i
$15$	0.748249	+	4.08059i	0.193197	+	1.05360i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	4.10222	+	7.10526i	0.994936	+	1.72328i	0.584516	+	0.811382i	$0.301284\pi$
$17$	4.10222	+	7.10526i	0.994936	+	1.72328i	0.410420	+	0.911897i	$0.365382\pi$
$18$	−0.480597	+	2.96125i	−0.113278	+	0.697974i
$19$	2.46823	−	4.27510i	0.566251	−	0.980776i	−0.430681	−	0.902504i	$-0.641727\pi$
$19$	2.46823	−	4.27510i	0.566251	−	0.980776i	0.996932	−	0.0782716i	$-0.0249401\pi$
$20$	−1.83484	+	1.53961i	−0.410282	+	0.344267i
$21$	1.71161	+	4.25093i	0.373504	+	0.927628i
$22$	−0.137179	+	0.777978i	−0.0292466	+	0.165866i
$23$	0.428299	−	2.42900i	0.0893065	−	0.506482i	−0.907037	−	0.421050i	$-0.861662\pi$
$23$	0.428299	−	2.42900i	0.0893065	−	0.506482i	0.996344	−	0.0854324i	$-0.0272272\pi$
$24$	−1.62352	+	0.603483i	−0.331399	+	0.123186i
$25$	0.564595	−	0.473751i	0.112919	−	0.0947502i
$26$	−0.346602	−	0.600332i	−0.0679742	−	0.117735i
$27$	2.50546	−	4.55221i	0.482177	−	0.876074i
$28$	−1.64553	+	2.07177i	−0.310976	+	0.391527i
$29$	3.76826	+	1.37153i	0.699748	+	0.254687i	0.667303	−	0.744786i	$-0.267449\pi$
$29$	3.76826	+	1.37153i	0.699748	+	0.254687i	0.0324444	+	0.999474i	$0.489671\pi$
$30$	3.88866	−	1.44547i	0.709969	−	0.263905i
$31$	5.43257	−	1.97729i	0.975718	−	0.355132i	0.195544	−	0.980695i	$-0.437353\pi$
$31$	5.43257	−	1.97729i	0.975718	−	0.355132i	0.780174	+	0.625562i	$0.215130\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	0.676045	−	1.18961i	0.117684	−	0.207084i
$34$	6.28497	−	5.27372i	1.07786	−	0.904435i
$35$	3.94139	−	4.96232i	0.666217	−	0.838785i
$36$	2.99972	−	0.0409212i	0.499953	−	0.00682020i
$37$	1.88252			0.309485			0.154742	−	0.987955i	$-0.450545\pi$
$37$	1.88252			0.309485			0.154742	+	0.987955i	$0.450545\pi$
$38$	−4.63876	−	1.68837i	−0.752506	−	0.273890i
$39$	0.216553	+	1.18097i	0.0346762	+	0.189107i
$40$	1.83484	+	1.53961i	0.290113	+	0.243434i
$41$	−11.7991	+	4.29451i	−1.84271	+	0.670690i	−0.854110	+	0.520092i	$0.825898\pi$
$41$	−11.7991	+	4.29451i	−1.84271	+	0.670690i	−0.988595	+	0.150598i	$0.951880\pi$
$42$	3.88913	−	2.42377i	0.600105	−	0.373997i
$43$	0.552932	+	3.13583i	0.0843213	+	0.478210i	0.997501	+	0.0706526i	$0.0225082\pi$
$43$	0.552932	+	3.13583i	0.0843213	+	0.478210i	−0.913180	+	0.407557i	$0.866381\pi$
$44$	0.789980			0.119094
$45$	−7.18496	+	0.0980148i	−1.07107	+	0.0146112i
$46$	−2.46647			−0.363662
$47$	−1.47259	−	0.535978i	−0.214799	−	0.0781805i	0.232379	−	0.972625i	$-0.425349\pi$
$47$	−1.47259	−	0.535978i	−0.214799	−	0.0781805i	−0.447179	+	0.894445i	$0.647571\pi$
$48$	0.876236	+	1.49406i	0.126474	+	0.215649i
$49$	3.16898	−	6.24160i	0.452711	−	0.891657i
$50$	−0.564595	−	0.473751i	−0.0798457	−	0.0669985i
$51$	−13.3201	+	4.95125i	−1.86518	+	0.693313i
$52$	−0.531025	+	0.445583i	−0.0736399	+	0.0617912i
$53$	−4.62037	+	8.00272i	−0.634657	+	1.09926i	0.351931	+	0.936026i	$0.385525\pi$
$53$	−4.62037	+	8.00272i	−0.634657	+	1.09926i	−0.986588	+	0.163232i	$0.947808\pi$
$54$	−4.91812	−	1.67692i	−0.669272	−	0.228199i
$55$	−1.89217			−0.255140
$56$	2.32604	+	1.26077i	0.310830	+	0.168478i
$57$	6.58717	+	5.45117i	0.872492	+	0.722025i
$58$	0.696346	−	3.94917i	0.0914346	−	0.518552i
$59$	−9.91385	−	8.31871i	−1.29067	−	1.08300i	−0.991677	−	0.128750i	$-0.958904\pi$
$59$	−9.91385	−	8.31871i	−1.29067	−	1.08300i	−0.298996	−	0.954254i	$-0.596652\pi$
$60$	−2.09877	−	3.57858i	−0.270950	−	0.461993i
$61$	2.49273	+	0.907280i	0.319162	+	0.116165i	0.496633	−	0.867961i	$-0.334569\pi$
$61$	2.49273	+	0.907280i	0.319162	+	0.116165i	−0.177471	+	0.984126i	$0.556792\pi$
$62$	−2.89061	−	5.00668i	−0.367108	−	0.635849i
$63$	−7.75439	+	1.69395i	−0.976961	+	0.213417i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	1.27192	−	1.06726i	0.157762	−	0.132378i
$66$	−1.28893	−	0.459201i	−0.158656	−	0.0565237i
$67$	0.213835	−	1.21272i	0.0261241	−	0.148157i	−0.968956	−	0.247235i	$-0.920478\pi$
$67$	0.213835	−	1.21272i	0.0261241	−	0.148157i	0.995080	+	0.0990776i	$0.0315892\pi$
$68$	−6.28497	−	5.27372i	−0.762165	−	0.639532i
$69$	4.02429	+	1.43372i	0.484468	+	0.172599i
$70$	−5.57134	−	3.01982i	−0.665903	−	0.360937i
$71$	−3.32517	+	5.75936i	−0.394625	+	0.683511i	−0.993053	−	0.117666i	$-0.962459\pi$
$71$	−3.32517	+	5.75936i	−0.394625	+	0.683511i	0.598428	+	0.801176i	$0.295792\pi$
$72$	−0.561196	−	2.94704i	−0.0661375	−	0.347312i
$73$	−7.17241			−0.839467			−0.419733	−	0.907647i	$-0.637876\pi$
$73$	−7.17241			−0.839467			−0.419733	+	0.907647i	$0.637876\pi$
$74$	−0.326897	−	1.85392i	−0.0380010	−	0.215514i
$75$	0.645809	+	1.10116i	0.0745716	+	0.127151i
$76$	−0.857208	+	4.86147i	−0.0983285	+	0.557649i
$77$	−2.04783	+	0.418167i	−0.233372	+	0.0476545i
$78$	1.12543	−	0.418337i	0.127430	−	0.0473673i
$79$	−1.70323	−	9.65951i	−0.191629	−	1.08678i	−0.917139	−	0.398568i	$-0.869507\pi$
$79$	−1.70323	−	9.65951i	−0.191629	−	1.08678i	0.725510	−	0.688212i	$-0.241604\pi$
$80$	1.19760	−	2.07431i	0.133896	−	0.231915i
$81$	7.04964	+	5.59487i	0.783294	+	0.621652i
$82$	6.27815	+	10.8741i	0.693306	+	1.20084i
$83$	−5.17113	−	1.88214i	−0.567605	−	0.206591i	0.0422463	−	0.999107i	$-0.486549\pi$
$83$	−5.17113	−	1.88214i	−0.567605	−	0.206591i	−0.609851	+	0.792516i	$0.708771\pi$
$84$	−3.06229	−	3.40916i	−0.334123	−	0.371970i
$85$	15.0538	+	12.6317i	1.63282	+	1.37010i
$86$	2.99218	−	1.08906i	0.322655	−	0.117437i
$87$	−3.43174	+	6.03869i	−0.367921	+	0.647415i
$88$	−0.137179	−	0.777978i	−0.0146233	−	0.0829328i
$89$	−1.28793	+	2.23076i	−0.136520	+	0.236460i	−0.926177	−	0.377089i	$-0.876925\pi$
$89$	−1.28793	+	2.23076i	−0.136520	+	0.236460i	0.789657	+	0.613549i	$0.210258\pi$
$90$	1.34418	+	7.05878i	0.141689	+	0.744061i
$91$	1.14069	−	1.43616i	0.119577	−	0.150550i
$92$	0.428299	+	2.42900i	0.0446532	+	0.253241i
$93$	1.80602	+	9.84915i	0.187276	+	1.02131i
$94$	−0.272123	+	1.54329i	−0.0280674	+	0.159178i
$95$	2.05319	−	11.6442i	0.210653	−	1.19467i
$96$	1.31920	−	1.12236i	0.134641	−	0.114551i
$97$	−2.83825	−	16.0965i	−0.288181	−	1.63435i	−0.693698	−	0.720266i	$-0.744020\pi$
$97$	−2.83825	−	16.0965i	−0.288181	−	1.63435i	0.405517	−	0.914088i	$-0.367092\pi$
$98$	−6.69706	−	2.03699i	−0.676506	−	0.205767i
$99$	1.83609	+	1.49846i	0.184534	+	0.150601i
$100$	−0.368513	+	0.638283i	−0.0368513	+	0.0638283i
$101$	−1.22157	−	6.92789i	−0.121551	−	0.689351i	−0.983297	−	0.182010i	$-0.941740\pi$
$101$	−1.22157	−	6.92789i	−0.121551	−	0.689351i	0.861745	−	0.507341i	$-0.169371\pi$
$102$	7.18903	+	12.2579i	0.711820	+	1.21372i
$103$	−10.0946	+	3.67412i	−0.994647	+	0.362022i	−0.787518	−	0.616292i	$-0.788634\pi$
$103$	−10.0946	+	3.67412i	−0.994647	+	0.362022i	−0.207129	+	0.978314i	$0.566412\pi$
$104$	0.531025	+	0.445583i	0.0520713	+	0.0436930i
$105$	7.33483	+	8.16565i	0.715806	+	0.796886i
$106$	8.68346	+	3.16052i	0.843412	+	0.306977i
$107$	4.53940	+	7.86247i	0.438840	+	0.760093i	0.997600	−	0.0692358i	$-0.0220561\pi$
$107$	4.53940	+	7.86247i	0.438840	+	0.760093i	−0.558760	+	0.829329i	$0.688723\pi$
$108$	−0.797416	+	5.13460i	−0.0767314	+	0.494077i
$109$	−9.29713	+	16.1031i	−0.890504	+	1.54240i	−0.0512312	+	0.998687i	$0.516315\pi$
$109$	−9.29713	+	16.1031i	−0.890504	+	1.54240i	−0.839273	+	0.543711i	$0.817019\pi$
$110$	0.328571	+	1.86342i	0.0313280	+	0.177670i
$111$	−0.544288	+	3.21488i	−0.0516615	+	0.305143i
$112$	0.837708	−	2.50963i	0.0791560	−	0.237138i
$113$	2.20476	−	12.5038i	0.207407	−	1.17626i	−0.686201	−	0.727412i	$-0.740723\pi$
$113$	2.20476	−	12.5038i	0.207407	−	1.17626i	0.893608	−	0.448849i	$-0.148166\pi$
$114$	4.22450	−	7.43368i	0.395661	−	0.696228i
$115$	−1.02587	−	5.81797i	−0.0956624	−	0.542529i
$116$	−4.01009			−0.372328
$117$	−2.07942	+	0.0283667i	−0.192242	+	0.00262251i
$118$	−6.47081	+	11.2078i	−0.595686	+	1.03176i
$119$	19.0839	+	10.3440i	1.74941	+	0.948229i
$120$	−3.15977	+	2.68830i	−0.288446	+	0.245407i
$121$	−7.94842	−	6.66952i	−0.722584	−	0.606320i
$122$	0.460638	−	2.61241i	0.0417042	−	0.236516i
$123$	−3.92252	−	21.3915i	−0.353682	−	1.92881i
$124$	−4.42867	+	3.71610i	−0.397706	+	0.333715i
$125$	−5.10536	+	8.84274i	−0.456637	+	0.790918i
$126$	3.01475	+	7.34243i	0.268575	+	0.654116i
$127$	−1.24093	−	2.14935i	−0.110114	−	0.190724i	0.805702	−	0.592321i	$-0.201788\pi$
$127$	−1.24093	−	2.14935i	−0.110114	−	0.190724i	−0.915816	+	0.401598i	$0.868455\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	−5.51508	+	0.0376157i	−0.485576	+	0.00331188i
$130$	−1.27192	−	1.06726i	−0.111554	−	0.0936052i
$131$	−2.83790	+	16.0945i	−0.247948	+	1.40618i	0.565597	+	0.824682i	$0.308646\pi$
$131$	−2.83790	+	16.0945i	−0.247948	+	1.40618i	−0.813545	+	0.581502i	$0.802465\pi$
$132$	−0.228404	+	1.34909i	−0.0198800	+	0.117423i
$133$	−0.351258	−	13.0559i	−0.0304579	−	1.13209i
$134$	−1.23143			−0.106379
$135$	1.90998	−	12.2984i	0.164385	−	1.05848i
$136$	−4.10222	+	7.10526i	−0.351763	+	0.609271i
$137$	−0.796805	+	0.668599i	−0.0680756	+	0.0571222i	−0.676191	−	0.736727i	$-0.736370\pi$
$137$	−0.796805	+	0.668599i	−0.0680756	+	0.0571222i	0.608115	+	0.793849i	$0.291926\pi$
$138$	0.713124	−	4.21212i	0.0607051	−	0.358559i
$139$	−7.97529	−	6.69206i	−0.676455	−	0.567613i	0.238513	−	0.971139i	$-0.423340\pi$
$139$	−7.97529	−	6.69206i	−0.676455	−	0.567613i	−0.914968	+	0.403526i	$0.867784\pi$
$140$	−2.00649	+	6.01109i	−0.169579	+	0.508030i
$141$	1.34108	−	2.35985i	0.112939	−	0.198735i
$142$	6.24927	+	2.27455i	0.524427	+	0.190876i
$143$	−0.547617			−0.0457940
$144$	−2.80482	+	1.06442i	−0.233735	+	0.0887015i
$145$	9.60501			0.797653
$146$	1.24548	+	7.06344i	0.103076	+	0.584575i
$147$	9.74285	+	7.21643i	0.803577	+	0.595201i
$148$	−1.76899	+	0.643861i	−0.145410	+	0.0529250i
$149$	13.7684	+	11.5531i	1.12795	+	0.946464i	0.998979	−	0.0451842i	$-0.0143875\pi$
$149$	13.7684	+	11.5531i	1.12795	+	0.946464i	0.128973	+	0.991648i	$0.458832\pi$
$150$	0.972287	−	0.827212i	0.0793869	−	0.0675416i
$151$	−5.43939	−	1.97977i	−0.442651	−	0.161112i	0.111073	−	0.993812i	$-0.464571\pi$
$151$	−5.43939	−	1.97977i	−0.442651	−	0.161112i	−0.553724	+	0.832701i	$0.686794\pi$
$152$	4.93646			0.400400
$153$	−4.60430	−	24.1789i	−0.372236	−	1.95474i
$154$	0.767416	+	1.94411i	0.0618402	+	0.156661i
$155$	10.6076	−	8.90083i	0.852022	−	0.714932i
$156$	−0.607410	−	1.03569i	−0.0486317	−	0.0829213i
$157$	8.51036	+	7.14104i	0.679201	+	0.569917i	0.915773	−	0.401697i	$-0.131579\pi$
$157$	8.51036	+	7.14104i	0.679201	+	0.569917i	−0.236572	+	0.971614i	$0.576024\pi$
$158$	−9.21700	+	3.35471i	−0.733265	+	0.266887i
$159$	−12.3308	−	10.2042i	−0.977893	−	0.809248i
$160$	−2.25076	−	0.819210i	−0.177938	−	0.0647642i
$161$	−2.39603	−	6.06989i	−0.188833	−	0.478374i
$162$	4.28571	−	7.91408i	0.336717	−	0.621789i
$163$	0.959873	+	1.66255i	0.0751830	+	0.130221i	0.901166	−	0.433474i	$-0.142713\pi$
$163$	0.959873	+	1.66255i	0.0751830	+	0.130221i	−0.825983	+	0.563695i	$0.809379\pi$
$164$	9.61869	−	8.07104i	0.751094	−	0.630242i
$165$	0.547076	−	3.23135i	0.0425898	−	0.251560i
$166$	−0.955586	+	5.41940i	−0.0741678	+	0.420627i
$167$	3.45177	−	19.5759i	0.267106	−	1.51483i	−0.495866	−	0.868399i	$-0.665149\pi$
$167$	3.45177	−	19.5759i	0.267106	−	1.51483i	0.762971	−	0.646432i	$-0.223740\pi$
$168$	−2.82561	+	3.60776i	−0.218000	+	0.278345i
$169$	−9.59047	+	8.04736i	−0.737728	+	0.619028i
$170$	9.82569	−	17.0186i	0.753596	−	1.30527i
$171$	−11.2137	+	9.67315i	−0.857537	+	0.739724i
$172$	−1.59210	−	2.75760i	−0.121397	−	0.210265i
$173$	2.09003	−	1.75374i	0.158902	−	0.133335i	−0.559870	−	0.828580i	$-0.689149\pi$
$173$	2.09003	−	1.75374i	0.158902	−	0.133335i	0.718772	+	0.695246i	$0.244704\pi$
$174$	6.54286	+	2.33099i	0.496013	+	0.176712i
$175$	0.617413	−	1.84966i	0.0466720	−	0.139821i
$176$	−0.742338	+	0.270189i	−0.0559559	+	0.0203663i
$177$	17.0726	−	14.5252i	1.28326	−	1.09178i
$178$	2.42051	+	0.880995i	0.181425	+	0.0660333i
$179$	0.868957	+	1.50508i	0.0649489	+	0.112495i	0.896671	−	0.442697i	$-0.145978\pi$
$179$	0.868957	+	1.50508i	0.0649489	+	0.112495i	−0.831722	+	0.555192i	$0.812645\pi$
$180$	6.71813	−	2.54950i	0.500740	−	0.190029i
$181$	−3.48243	−	6.03175i	−0.258847	−	0.448336i	0.707086	−	0.707127i	$-0.250009\pi$
$181$	−3.48243	−	6.03175i	−0.258847	−	0.448336i	−0.965933	+	0.258791i	$0.916676\pi$
$182$	−1.61242	−	0.873974i	−0.119520	−	0.0647832i
$183$	−2.27012	+	3.99464i	−0.167812	+	0.295292i
$184$	2.31773	−	0.843584i	0.170865	−	0.0621898i
$185$	4.23711	−	1.54218i	0.311518	−	0.113383i
$186$	9.38591	−	3.48887i	0.688208	−	0.255816i
$187$	−1.12547	−	6.38288i	−0.0823029	−	0.466763i
$188$	1.56710			0.114292
$189$	−0.650833	−	13.7323i	−0.0473412	−	0.998879i
$190$	−11.8239			−0.857793
$191$	0.890954	+	5.05285i	0.0644672	+	0.365611i	0.999926	+	0.0121755i	$0.00387567\pi$
$191$	0.890954	+	5.05285i	0.0644672	+	0.365611i	−0.935459	+	0.353436i	$0.885013\pi$
$192$	−1.33439	−	1.10427i	−0.0963013	−	0.0796935i
$193$	14.6321	−	5.32566i	1.05324	−	0.383349i	0.243357	−	0.969937i	$-0.421751\pi$
$193$	14.6321	−	5.32566i	1.05324	−	0.383349i	0.809886	+	0.586588i	$0.199529\pi$
$194$	−15.3591	+	5.59026i	−1.10272	+	0.401357i
$195$	1.45487	+	2.48069i	0.104186	+	0.177646i
$196$	−0.843112	+	6.94904i	−0.0602223	+	0.496360i
$197$	−8.03870	−	13.9234i	−0.572734	−	0.992004i	−0.996284	−	0.0861314i	$-0.972550\pi$
$197$	−8.03870	−	13.9234i	−0.572734	−	0.992004i	0.423550	−	0.905873i	$-0.360784\pi$
$198$	1.15686	−	2.06840i	0.0822147	−	0.146995i
$199$	9.14931	+	15.8471i	0.648577	+	1.12337i	0.983463	+	0.181110i	$0.0579690\pi$
$199$	9.14931	+	15.8471i	0.648577	+	1.12337i	−0.334886	+	0.942259i	$0.608698\pi$
$200$	0.692578	+	0.252078i	0.0489727	+	0.0178246i
$201$	2.00919	+	0.715806i	0.141718	+	0.0504890i
$202$	−6.61052	+	2.40603i	−0.465114	+	0.169288i
$203$	10.3952	−	2.12270i	0.729600	−	0.148984i
$204$	10.8233	−	9.20838i	0.757785	−	0.644716i
$205$	−23.0388	+	19.3318i	−1.60910	+	1.35019i
$206$	5.37120	+	9.30320i	0.374230	+	0.648185i
$207$	−3.61196	+	6.45796i	−0.251048	+	0.448859i
$208$	0.346602	−	0.600332i	0.0240325	−	0.0416255i
$209$	−2.98735	+	2.50668i	−0.206639	+	0.173391i
$210$	6.76792	−	8.64135i	0.467031	−	0.596310i
$211$	−2.32062	+	13.1609i	−0.159758	+	0.906031i	0.794548	+	0.607201i	$0.207708\pi$
$211$	−2.32062	+	13.1609i	−0.159758	+	0.906031i	−0.954306	+	0.298831i	$0.903403\pi$
$212$	1.60464	−	9.10035i	0.110207	−	0.625015i
$213$	−8.87415	−	7.34374i	−0.608047	−	0.503185i
$214$	6.95476	−	5.83574i	0.475418	−	0.398923i
$215$	3.81342	+	6.60504i	0.260073	+	0.450460i
$216$	5.19506	−	0.106312i	0.353479	−	0.00723363i
$217$	9.51319	−	11.9773i	0.645797	−	0.813075i
$218$	17.4729	+	6.35961i	1.18341	+	0.430727i
$219$	2.07373	−	12.2487i	0.140130	−	0.827688i
$220$	1.77806	−	0.647159i	0.119876	−	0.0436315i
$221$	4.35677	+	3.65576i	0.293068	+	0.245913i
$222$	3.26055	−	0.0222386i	0.218834	−	0.00149256i
$223$	12.9301	−	10.8496i	0.865863	−	0.726545i	−0.0973597	−	0.995249i	$-0.531040\pi$
$223$	12.9301	−	10.8496i	0.865863	−	0.726545i	0.963223	+	0.268704i	$0.0865953\pi$
$224$	−2.61697	−	0.389189i	−0.174854	−	0.0260038i
$225$	−2.06723	+	0.784504i	−0.137815	+	0.0523003i
$226$	−12.6967			−0.844573
$227$	−12.9131	−	4.69997i	−0.857070	−	0.311948i	−0.124150	−	0.992263i	$-0.539621\pi$
$227$	−12.9131	−	4.69997i	−0.857070	−	0.311948i	−0.732919	+	0.680315i	$0.761843\pi$
$228$	−8.05432	−	2.86948i	−0.533411	−	0.190036i
$229$	8.72645	+	7.32236i	0.576660	+	0.483875i	0.883848	−	0.467773i	$-0.154944\pi$
$229$	8.72645	+	7.32236i	0.576660	+	0.483875i	−0.307188	+	0.951649i	$0.599388\pi$
$230$	−5.55144	+	2.02056i	−0.366051	+	0.133232i
$231$	−0.122041	−	3.61809i	−0.00802970	−	0.238053i
$232$	0.696346	+	3.94917i	0.0457173	+	0.259276i
$233$	3.13321			0.205263			0.102632	−	0.994719i	$-0.467274\pi$
$233$	3.13321			0.205263			0.102632	+	0.994719i	$0.467274\pi$
$234$	0.389023	+	2.04290i	0.0254312	+	0.133549i
$235$	−3.75352			−0.244853
$236$	12.1611	+	4.42629i	0.791623	+	0.288127i
$237$	16.9885	−	0.115870i	1.10352	−	0.00752658i
$238$	6.87294	−	20.5901i	0.445506	−	1.33466i
$239$	−4.76265	−	3.99634i	−0.308070	−	0.258502i	0.475624	−	0.879649i	$-0.342222\pi$
$239$	−4.76265	−	3.99634i	−0.308070	−	0.258502i	−0.783694	+	0.621147i	$0.786667\pi$
$240$	3.19614	+	2.64495i	0.206310	+	0.170731i
$241$	20.1388	−	16.8985i	1.29726	−	1.08853i	0.306643	−	0.951824i	$-0.400794\pi$
$241$	20.1388	−	16.8985i	1.29726	−	1.08853i	0.990612	−	0.136702i	$-0.0436503\pi$
$242$	−5.18797	+	8.98582i	−0.333495	+	0.577630i
$243$	−11.5929	+	10.4214i	−0.743683	+	0.668533i
$244$	−2.65271			−0.169822
$245$	2.01943	−	16.6444i	0.129017	−	1.06337i
$246$	−20.3854	+	7.57752i	−1.29972	+	0.483125i
$247$	0.594220	−	3.36999i	0.0378093	−	0.214427i
$248$	4.42867	+	3.71610i	0.281221	+	0.235972i
$249$	4.70933	−	8.28681i	0.298441	−	0.525155i
$250$	9.59493	+	3.49227i	0.606837	+	0.220871i
$251$	14.2337	+	24.6536i	0.898426	+	1.55612i	0.829507	+	0.558496i	$0.188622\pi$
$251$	14.2337	+	24.6536i	0.898426	+	1.55612i	0.0689187	+	0.997622i	$0.478045\pi$
$252$	6.70738	−	4.24395i	0.422525	−	0.267343i
$253$	−0.974233	+	1.68742i	−0.0612495	+	0.106087i
$254$	−1.90121	+	1.59530i	−0.119292	+	0.100098i
$255$	−25.9242	+	22.0560i	−1.62343	+	1.38120i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	14.6534	+	12.2957i	0.914055	+	0.766983i	0.972886	−	0.231285i	$-0.0742929\pi$
$257$	14.6534	+	12.2957i	0.914055	+	0.766983i	−0.0588311	+	0.998268i	$0.518737\pi$
$258$	0.994728	+	5.42476i	0.0619290	+	0.337731i
$259$	4.24487	−	2.60545i	0.263763	−	0.161895i
$260$	−0.830184	+	1.43792i	−0.0514858	+	0.0891761i
$261$	−9.32035	−	7.60649i	−0.576915	−	0.470830i
$262$	16.3428			1.00966
$263$	1.70456	+	9.66704i	0.105108	+	0.596095i	0.991177	+	0.132543i	$0.0423142\pi$
$263$	1.70456	+	9.66704i	0.105108	+	0.596095i	−0.886070	+	0.463552i	$0.846575\pi$
$264$	1.36825	−	0.00933220i	0.0842102	−	0.000574357i
$265$	−3.84344	+	21.7973i	−0.236101	+	1.33899i
$266$	−12.7966	+	2.61306i	−0.784609	+	0.160217i
$267$	−3.43720	−	2.84443i	−0.210353	−	0.174076i
$268$	0.213835	+	1.21272i	0.0130620	+	0.0740786i
$269$	−0.530630	+	0.919078i	−0.0323531	+	0.0560372i	−0.881749	−	0.471720i	$-0.843633\pi$
$269$	−0.530630	+	0.919078i	−0.0323531	+	0.0560372i	0.849395	+	0.527757i	$0.176967\pi$
$270$	−12.4433	+	0.254640i	−0.757273	+	0.0154969i
$271$	−14.7949	−	25.6255i	−0.898724	−	1.55664i	−0.829126	−	0.559061i	$-0.811162\pi$
$271$	−14.7949	−	25.6255i	−0.898724	−	1.55664i	−0.0695979	−	0.997575i	$-0.522172\pi$
$272$	7.70966	+	2.80609i	0.467467	+	0.170144i
$273$	2.12279	+	2.36324i	0.128477	+	0.143030i
$274$	0.796805	+	0.668599i	0.0481368	+	0.0403915i
$275$	−0.547123	+	0.199136i	−0.0329927	+	0.0120084i
$276$	−4.27196	+	0.0291370i	−0.257142	+	0.00175384i
$277$	3.77703	+	21.4206i	0.226940	+	1.28704i	0.858942	+	0.512073i	$0.171122\pi$
$277$	3.77703	+	21.4206i	0.226940	+	1.28704i	−0.632002	+	0.774967i	$0.717767\pi$
$278$	−5.20550	+	9.01619i	−0.312205	+	0.540755i
$279$	−17.3420	+	0.236574i	−1.03824	+	0.0141633i
$280$	6.26819	+	0.932189i	0.374596	+	0.0557089i
$281$	−0.698979	−	3.96411i	−0.0416976	−	0.236479i	0.956835	−	0.290631i	$-0.0938653\pi$
$281$	−0.698979	−	3.96411i	−0.0416976	−	0.236479i	−0.998533	+	0.0541527i	$0.982754\pi$
$282$	−2.55687	−	0.910924i	−0.152259	−	0.0542447i
$283$	−2.61012	+	14.8027i	−0.155155	+	0.879930i	0.803488	+	0.595321i	$0.202975\pi$
$283$	−2.61012	+	14.8027i	−0.155155	+	0.879930i	−0.958644	+	0.284609i	$0.908136\pi$
$284$	1.15482	−	6.54931i	0.0685259	−	0.388630i
$285$	19.2918	+	6.87299i	1.14275	+	0.407121i
$286$	0.0950927	+	0.539298i	0.00562295	+	0.0318893i
$287$	−20.6618	+	26.0138i	−1.21963	+	1.53554i
$288$	1.53530	+	2.57737i	0.0904684	+	0.151873i
$289$	−25.1565	+	43.5723i	−1.47979	+	2.56308i
$290$	−1.66789	−	9.45909i	−0.0979421	−	0.555457i
$291$	28.3094	−	0.193085i	1.65953	−	0.0113188i
$292$	6.73986	−	2.45311i	0.394420	−	0.143557i
$293$	6.07018	+	5.09348i	0.354623	+	0.297564i	0.802643	−	0.596459i	$-0.203426\pi$
$293$	6.07018	+	5.09348i	0.354623	+	0.297564i	−0.448020	+	0.894024i	$0.647871\pi$
$294$	5.41497	−	10.8480i	0.315807	−	0.632666i
$295$	−29.1285	−	10.6019i	−1.69593	−	0.617266i
$296$	0.941261	+	1.63031i	0.0547097	+	0.0947600i
$297$	−3.08986	+	2.70233i	−0.179292	+	0.156805i
$298$	8.98669	−	15.5654i	0.520585	−	0.901680i
$299$	−0.296898	−	1.68379i	−0.0171701	−	0.0973763i
$300$	−0.983480	−	0.813872i	−0.0567813	−	0.0469889i
$301$	5.58685	+	6.30566i	0.322021	+	0.363452i
$302$	−1.00516	+	5.70053i	−0.0578403	+	0.328029i
$303$	12.1843	−	0.0831032i	0.699969	−	0.00477415i
$304$	−0.857208	−	4.86147i	−0.0491642	−	0.278824i
$305$	6.35380			0.363817
$306$	−23.0120	+	8.73297i	−1.31551	+	0.499230i
$307$	10.4904	−	18.1700i	0.598722	−	1.03702i	−0.394289	−	0.918987i	$-0.629009\pi$
$307$	10.4904	−	18.1700i	0.598722	−	1.03702i	0.993010	−	0.118029i	$-0.0376577\pi$
$308$	1.78131	−	1.09335i	0.101500	−	0.0622993i
$309$	−3.35587	−	18.3013i	−0.190909	−	1.04112i
$310$	−10.6076	−	8.90083i	−0.602471	−	0.505533i
$311$	1.52506	−	8.64906i	0.0864784	−	0.490443i	−0.910549	−	0.413400i	$-0.864341\pi$
$311$	1.52506	−	8.64906i	0.0864784	−	0.490443i	0.997028	−	0.0770430i	$-0.0245479\pi$
$312$	−0.914477	+	0.778027i	−0.0517721	+	0.0440471i
$313$	−23.8274	+	19.9935i	−1.34680	+	1.13010i	−0.366980	+	0.930229i	$0.619608\pi$
$313$	−23.8274	+	19.9935i	−1.34680	+	1.13010i	−0.979822	+	0.199872i	$0.935947\pi$
$314$	5.55474	−	9.62110i	0.313472	−	0.542950i
$315$	−16.0656	+	10.1651i	−0.905192	+	0.572741i
$316$	4.90426	+	8.49443i	0.275886	+	0.477849i
$317$	−19.5898	−	7.13012i	−1.10028	−	0.400467i	−0.272858	−	0.962054i	$-0.587969\pi$
$317$	−19.5898	−	7.13012i	−1.10028	−	0.400467i	−0.827418	+	0.561587i	$0.810191\pi$
$318$	−7.90799	+	13.9154i	−0.443458	+	0.780335i
$319$	−2.42675	−	2.03628i	−0.135872	−	0.114010i
$320$	−0.415924	+	2.35882i	−0.0232508	+	0.131862i
$321$	−14.7396	+	5.47890i	−0.822683	+	0.305802i
$322$	−5.56161	+	3.41365i	−0.309936	+	0.190235i
$323$	40.5010			2.25353
$324$	−8.53805	−	2.84634i	−0.474336	−	0.158130i
$325$	0.255455	−	0.442460i	0.0141701	−	0.0245433i
$326$	1.47061	−	1.23399i	0.0814496	−	0.0683443i
$327$	−24.8120	−	20.5330i	−1.37211	−	1.13548i
$328$	−9.61869	−	8.07104i	−0.531103	−	0.445649i
$329$	−4.06232	+	0.829524i	−0.223963	+	0.0457332i
$330$	−3.27725	+	0.0223526i	−0.180407	+	0.00123047i
$331$	0.544302	+	0.198110i	0.0299175	+	0.0108891i	0.356936	−	0.934129i	$-0.383822\pi$
$331$	0.544302	+	0.198110i	0.0299175	+	0.0108891i	−0.327018	+	0.945018i	$0.606044\pi$
$332$	5.50300			0.302016
$333$	−5.33283	−	1.85901i	−0.292237	−	0.101873i
$334$	−19.8779			−1.08767
$335$	−0.512179	−	2.90471i	−0.0279834	−	0.158701i
$336$	4.04361	+	2.15620i	0.220597	+	0.117630i
$337$	4.66316	−	1.69725i	0.254019	−	0.0924552i	−0.211872	−	0.977297i	$-0.567956\pi$
$337$	4.66316	−	1.69725i	0.254019	−	0.0924552i	0.465891	+	0.884842i	$0.345734\pi$
$338$	9.59047	+	8.04736i	0.521653	+	0.437719i
$339$	20.7159	+	7.38037i	1.12514	+	0.400847i
$340$	−18.4662	−	6.72116i	−1.00147	−	0.364506i
$341$	−4.56705			−0.247319
$342$	11.4734	+	9.36366i	0.620413	+	0.506329i
$343$	−1.49283	−	18.4600i	−0.0806053	−	0.996746i
$344$	−2.43924	+	2.04677i	−0.131515	+	0.110354i
$345$	10.2322	−	0.0697892i	0.550885	−	0.00375732i
$346$	−2.09003	−	1.75374i	−0.112361	−	0.0942819i
$347$	19.9642	−	7.26637i	1.07173	−	0.390079i	0.254909	−	0.966965i	$-0.417954\pi$
$347$	19.9642	−	7.26637i	1.07173	−	0.390079i	0.816825	+	0.576886i	$0.195732\pi$
$348$	1.15943	−	6.84823i	0.0621517	−	0.367104i
$349$	11.3844	+	4.14359i	0.609393	+	0.221801i	0.628238	−	0.778021i	$-0.283776\pi$
$349$	11.3844	+	4.14359i	0.609393	+	0.221801i	−0.0188444	+	0.999822i	$0.505999\pi$
$350$	−1.92877	−	0.286842i	−0.103097	−	0.0153324i
$351$	0.552772	−	3.55933i	0.0295048	−	0.189983i
$352$	0.394990	+	0.684143i	0.0210530	+	0.0364649i
$353$	18.6772	−	15.6721i	0.994090	−	0.834140i	0.00793490	−	0.999969i	$-0.497474\pi$
$353$	18.6772	−	15.6721i	0.994090	−	0.834140i	0.986155	+	0.165828i	$0.0530298\pi$
$354$	−17.2692	−	14.2910i	−0.917846	−	0.759557i
$355$	−2.76603	+	15.6870i	−0.146806	+	0.832577i
$356$	0.447293	−	2.53672i	0.0237065	−	0.134446i
$357$	−23.1825	+	29.5997i	−1.22695	+	1.56658i
$358$	1.33132	−	1.11711i	0.0703625	−	0.0590411i
$359$	−2.60795	+	4.51711i	−0.137643	+	0.238404i	−0.926604	−	0.376039i	$-0.877286\pi$
$359$	−2.60795	+	4.51711i	−0.137643	+	0.238404i	0.788961	+	0.614443i	$0.210619\pi$
$360$	−3.67736	−	6.17335i	−0.193814	−	0.325364i
$361$	−2.68434	−	4.64941i	−0.141281	−	0.244706i
$362$	−5.33540	+	4.47693i	−0.280422	+	0.235302i
$363$	13.6880	−	11.6456i	0.718432	−	0.611234i
$364$	−0.580703	+	1.73969i	−0.0304371	+	0.0911843i
$365$	−16.1434	+	5.87571i	−0.844983	+	0.307549i
$366$	4.32816	+	1.54197i	0.226236	+	0.0806002i
$367$	−35.0893	−	12.7715i	−1.83165	−	0.666665i	−0.992421	−	0.122880i	$-0.960787\pi$
$367$	−35.0893	−	12.7715i	−1.83165	−	0.666665i	−0.839225	−	0.543784i	$-0.816991\pi$
$368$	−1.23324	−	2.13603i	−0.0642869	−	0.111348i
$369$	37.6654	−	0.513819i	1.96078	−	0.0267484i
$370$	−2.25452	−	3.90494i	−0.117207	−	0.203008i
$371$	0.657533	+	24.4399i	0.0341374	+	1.26885i
$372$	−5.06571	−	8.63748i	−0.262645	−	0.447833i
$373$	11.3692	−	4.13806i	0.588676	−	0.214261i	−0.0304708	−	0.999536i	$-0.509701\pi$
$373$	11.3692	−	4.13806i	0.588676	−	0.214261i	0.619147	+	0.785275i	$0.287478\pi$
$374$	−6.09048	+	2.21675i	−0.314931	+	0.114626i
$375$	−13.6251	−	11.2753i	−0.703596	−	0.582256i
$376$	−0.272123	−	1.54329i	−0.0140337	−	0.0795890i
$377$	2.77981			0.143168
$378$	−13.4107	+	3.02554i	−0.689771	+	0.155617i
$379$	−3.34155			−0.171644			−0.0858220	−	0.996310i	$-0.527352\pi$
$379$	−3.34155			−0.171644			−0.0858220	+	0.996310i	$0.527352\pi$
$380$	2.05319	+	11.6442i	0.105327	+	0.597336i
$381$	4.02933	−	1.49776i	0.206429	−	0.0767324i
$382$	4.82137	−	1.75484i	0.246683	−	0.0897853i
$383$	−1.85388	+	0.674757i	−0.0947288	+	0.0344785i	−0.388950	−	0.921259i	$-0.627162\pi$
$383$	−1.85388	+	0.674757i	−0.0947288	+	0.0344785i	0.294221	+	0.955737i	$0.404940\pi$
$384$	−0.855775	+	1.50587i	−0.0436711	+	0.0768462i
$385$	−4.26661	+	2.61880i	−0.217447	+	0.133466i
$386$	−7.78559	−	13.4850i	−0.396276	−	0.686370i
$387$	1.53032	−	9.42924i	0.0777905	−	0.479315i
$388$	8.17242	+	14.1550i	0.414892	+	0.718613i
$389$	−8.27749	−	3.01276i	−0.419685	−	0.152753i	0.123541	−	0.992340i	$-0.460575\pi$
$389$	−8.27749	−	3.01276i	−0.419685	−	0.152753i	−0.543226	+	0.839587i	$0.682797\pi$
$390$	2.19036	−	1.86354i	0.110913	−	0.0943639i
$391$	19.0157	−	6.92114i	0.961664	−	0.350017i
$392$	6.98987	−	0.376385i	0.353042	−	0.0190103i
$393$	−26.6649	−	9.49977i	−1.34507	−	0.479200i
$394$	−12.3160	+	10.3344i	−0.620472	+	0.520637i
$395$	−11.7467	−	20.3459i	−0.591042	−	1.02372i
$396$	−2.23786	−	0.780114i	−0.112457	−	0.0392022i
$397$	15.5860	−	26.9958i	0.782240	−	1.35488i	−0.148394	−	0.988928i	$-0.547411\pi$
$397$	15.5860	−	26.9958i	0.782240	−	1.35488i	0.930634	−	0.365951i	$-0.119256\pi$
$398$	14.0176	−	11.7621i	0.702636	−	0.589582i
$399$	22.3978	+	3.17496i	1.12129	+	0.158947i
$400$	0.127983	−	0.725829i	0.00639916	−	0.0362914i
$401$	−2.53565	+	14.3804i	−0.126624	+	0.718121i	0.853706	+	0.520755i	$0.174350\pi$
$401$	−2.53565	+	14.3804i	−0.126624	+	0.718121i	−0.980330	+	0.197365i	$0.936761\pi$
$402$	0.356038	−	2.10297i	0.0177576	−	0.104886i
$403$	3.06997	−	2.57601i	0.152926	−	0.128320i
$404$	3.51738	+	6.09229i	0.174996	+	0.303103i
$405$	20.4504	+	6.81757i	1.01619	+	0.338768i
$406$	−3.89556	−	9.86867i	−0.193333	−	0.489774i
$407$	−1.39747	−	0.508637i	−0.0692700	−	0.0252122i
$408$	−10.9479	−	9.05989i	−0.542004	−	0.448531i
$409$	−2.29495	+	0.835292i	−0.113478	+	0.0413025i	−0.398135	−	0.917327i	$-0.630342\pi$
$409$	−2.29495	+	0.835292i	−0.113478	+	0.0413025i	0.284657	+	0.958629i	$0.408120\pi$
$410$	23.0388	+	19.3318i	1.13780	+	0.954731i
$411$	−0.911421	−	1.55405i	−0.0449571	−	0.0766558i
$412$	8.22916	−	6.90509i	0.405422	−	0.340189i
$413$	−33.8678	−	5.03673i	−1.66653	−	0.247841i
$414$	6.98706	+	2.43567i	0.343395	+	0.119707i
$415$	−13.1808			−0.647022
$416$	−0.651399	−	0.237090i	−0.0319374	−	0.0116243i
$417$	13.7342	−	11.6849i	0.672568	−	0.572214i
$418$	2.98735	+	2.50668i	0.146116	+	0.122606i
$419$	−10.9707	+	3.99299i	−0.535951	+	0.195070i	−0.595794	−	0.803137i	$-0.703162\pi$
$419$	−10.9707	+	3.99299i	−0.535951	+	0.195070i	0.0598423	+	0.998208i	$0.480940\pi$
$420$	−9.68530	−	5.16454i	−0.472594	−	0.252004i
$421$	4.38782	+	24.8846i	0.213849	+	1.21280i	0.882892	+	0.469576i	$0.155593\pi$
$421$	4.38782	+	24.8846i	0.213849	+	1.21280i	−0.669043	+	0.743224i	$0.733296\pi$
$422$	13.3639			0.650544
$423$	3.64228	+	2.97252i	0.177094	+	0.144529i
$424$	−9.24074			−0.448770
$425$	5.68222	+	2.06816i	0.275628	+	0.100320i
$426$	−5.69119	+	10.0146i	−0.275739	+	0.485207i
$427$	6.87651	−	1.40418i	0.332778	−	0.0679531i
$428$	−6.95476	−	5.83574i	−0.336171	−	0.282081i
$429$	0.158331	−	0.935192i	0.00764428	−	0.0451515i
$430$	5.84250	−	4.90244i	0.281750	−	0.236417i
$431$	−12.4657	+	21.5912i	−0.600451	+	1.04001i	0.392302	+	0.919837i	$0.371679\pi$
$431$	−12.4657	+	21.5912i	−0.600451	+	1.04001i	−0.992753	+	0.120175i	$0.961654\pi$
$432$	−1.00681	−	5.09768i	−0.0484402	−	0.245262i
$433$	−26.9371			−1.29451			−0.647257	−	0.762272i	$-0.724084\pi$
$433$	−26.9371			−1.29451			−0.647257	+	0.762272i	$0.724084\pi$
$434$	−13.4473	−	7.28881i	−0.645493	−	0.349874i
$435$	−2.77707	+	16.4029i	−0.133150	+	0.786461i
$436$	3.22886	−	18.3118i	0.154634	−	0.876975i
$437$	−9.32710	−	7.82636i	−0.446176	−	0.374386i
$438$	−12.4227	+	0.0847291i	−0.593579	+	0.00404852i
$439$	18.5796	+	6.76241i	0.886754	+	0.322752i	0.744932	−	0.667140i	$-0.232482\pi$
$439$	18.5796	+	6.76241i	0.886754	+	0.322752i	0.141822	+	0.989892i	$0.454704\pi$
$440$	−0.946083	−	1.63866i	−0.0451028	−	0.0781203i
$441$	−15.1408	+	14.5519i	−0.720989	+	0.692946i
$442$	2.84368	−	4.92539i	0.135260	−	0.234277i
$443$	9.65486	−	8.10139i	0.458716	−	0.384909i	−0.383942	−	0.923357i	$-0.625434\pi$
$443$	9.65486	−	8.10139i	0.458716	−	0.384909i	0.842658	+	0.538448i	$0.180989\pi$
$444$	−0.588089	−	3.20715i	−0.0279095	−	0.152205i
$445$	−1.07136	+	6.07598i	−0.0507873	+	0.288029i
$446$	−12.9301	−	10.8496i	−0.612258	−	0.513745i
$447$	−23.7105	+	20.1727i	−1.12147	+	0.954135i
$448$	0.0711558	+	2.64479i	0.00336180	+	0.124955i
$449$	−0.967788	+	1.67626i	−0.0456727	+	0.0791075i	−0.887958	−	0.459924i	$-0.847876\pi$
$449$	−0.967788	+	1.67626i	−0.0456727	+	0.0791075i	0.842285	+	0.539032i	$0.181210\pi$
$450$	1.13156	+	1.89959i	0.0533420	+	0.0895476i
$451$	9.91923			0.467078
$452$	2.20476	+	12.5038i	0.103703	+	0.588131i
$453$	4.95363	−	8.71670i	0.232742	−	0.409546i
$454$	−2.38624	+	13.5330i	−0.111992	+	0.635136i
$455$	1.39090	−	4.16691i	0.0652066	−	0.195348i
$456$	−1.42726	+	8.43024i	−0.0668377	+	0.394782i
$457$	2.14656	+	12.1737i	0.100412	+	0.569463i	0.992954	+	0.118500i	$0.0378085\pi$
$457$	2.14656	+	12.1737i	0.100412	+	0.569463i	−0.892542	+	0.450964i	$0.851080\pi$
$458$	5.69579	−	9.86539i	0.266147	−	0.460980i
$459$	42.6226	−	0.872234i	1.98945	−	0.0407124i
$460$	2.95386	+	5.11624i	0.137724	+	0.238546i
$461$	−31.5405	−	11.4798i	−1.46899	−	0.534668i	−0.521163	−	0.853457i	$-0.674502\pi$
$461$	−31.5405	−	11.4798i	−1.46899	−	0.534668i	−0.947826	+	0.318789i	$0.896724\pi$
$462$	−3.54193	+	0.748461i	−0.164785	+	0.0348215i
$463$	1.90685	+	1.60004i	0.0886187	+	0.0743599i	0.686021	−	0.727582i	$-0.259356\pi$
$463$	1.90685	+	1.60004i	0.0886187	+	0.0743599i	−0.597402	+	0.801942i	$0.703800\pi$
$464$	3.76826	−	1.37153i	0.174937	−	0.0636718i
$465$	12.1334	+	20.6886i	0.562675	+	0.959410i
$466$	−0.544076	−	3.08561i	−0.0252038	−	0.142938i
$467$	4.71146	−	8.16048i	0.218020	−	0.377622i	−0.736182	−	0.676783i	$-0.763373\pi$
$467$	4.71146	−	8.16048i	0.218020	−	0.377622i	0.954203	+	0.299161i	$0.0967068\pi$
$468$	1.94431	−	0.737859i	0.0898758	−	0.0341075i
$469$	−1.19625	−	3.03049i	−0.0552379	−	0.139935i
$470$	0.651792	+	3.69650i	0.0300649	+	0.170507i
$471$	−14.6557	+	12.4689i	−0.675298	+	0.574536i
$472$	2.24729	−	12.7450i	0.103440	−	0.586636i
$473$	0.436805	−	2.47724i	0.0200843	−	0.113904i
$474$	−3.06413	−	16.7103i	−0.140740	−	0.767528i
$475$	−0.631785	−	3.58303i	−0.0289883	−	0.164401i
$476$	−21.4708	−	3.19308i	−0.984112	−	0.146355i
$477$	20.9914	−	18.1075i	0.961131	−	0.829086i
$478$	−3.10860	+	5.38425i	−0.142184	+	0.246270i
$479$	−3.10543	−	17.6118i	−0.141891	−	0.804702i	−0.969811	−	0.243857i	$-0.921587\pi$
$479$	−3.10543	−	17.6118i	−0.141891	−	0.804702i	0.827921	−	0.560845i	$-0.189524\pi$
$480$	2.04976	−	3.60688i	0.0935583	−	0.164631i
$481$	1.22627	−	0.446327i	0.0559132	−	0.0203507i
$482$	−20.1388	−	16.8985i	−0.917298	−	0.769705i
$483$	11.0586	−	2.33684i	0.503184	−	0.106330i
$484$	9.75019	+	3.54878i	0.443190	+	0.161308i
$485$	−19.5746	−	33.9043i	−0.888839	−	1.53951i
$486$	12.2761	+	9.60709i	0.556857	+	0.435787i
$487$	3.99649	−	6.92212i	0.181098	−	0.313671i	−0.761157	−	0.648568i	$-0.775368\pi$
$487$	3.99649	−	6.92212i	0.181098	−	0.313671i	0.942255	+	0.334897i	$0.108702\pi$
$488$	0.460638	+	2.61241i	0.0208521	+	0.118258i
$489$	−3.11674	+	1.15853i	−0.140944	+	0.0523907i
$490$	−16.7422	+	0.901521i	−0.756336	+	0.0407266i
$491$	−0.834706	+	4.73385i	−0.0376697	+	0.213636i	−0.997832	−	0.0658058i	$-0.979038\pi$
$491$	−0.834706	+	4.73385i	−0.0376697	+	0.213636i	0.960163	+	0.279442i	$0.0901493\pi$
$492$	11.0023	+	18.7599i	0.496021	+	0.845760i
$493$	5.71313	+	32.4008i	0.257306	+	1.45926i
$494$	−3.42198			−0.153962
$495$	5.36015	+	1.86854i	0.240921	+	0.0839845i
$496$	2.89061	−	5.00668i	0.129792	−	0.224807i
$497$	0.473210	+	17.5888i	0.0212264	+	0.788965i
$498$	−8.97868	−	3.19879i	−0.402344	−	0.143341i
$499$	26.9417	+	22.6068i	1.20608	+	1.01202i	0.999435	+	0.0336020i	$0.0106979\pi$
$499$	26.9417	+	22.6068i	1.20608	+	1.01202i	0.206642	+	0.978417i	$0.433747\pi$
$500$	1.77307	−	10.0556i	0.0792942	−	0.449700i
$501$	32.4328	+	11.5547i	1.44899	+	0.516225i
$502$	21.8074	−	18.2985i	0.973310	−	0.816704i
$503$	−6.67662	+	11.5643i	−0.297696	+	0.515625i	−0.975608	−	0.219518i	$-0.929551\pi$
$503$	−6.67662	+	11.5643i	−0.297696	+	0.515625i	0.677912	+	0.735143i	$0.262885\pi$
$504$	−5.34419	−	5.86852i	−0.238049	−	0.261405i
$505$	−8.42487	−	14.5923i	−0.374902	−	0.649349i
$506$	1.83096	+	0.666414i	0.0813960	+	0.0296257i
$507$	−10.9700	−	18.7048i	−0.487195	−	0.830710i
$508$	1.90121	+	1.59530i	0.0843525	+	0.0707801i
$509$	6.29786	−	35.7170i	0.279148	−	1.58313i	−0.446322	−	0.894873i	$-0.647266\pi$
$509$	6.29786	−	35.7170i	0.279148	−	1.58313i	0.725470	−	0.688254i	$-0.241623\pi$
$510$	26.2226	+	21.7003i	1.16116	+	0.960907i
$511$	−16.1729	+	9.92675i	−0.715448	+	0.439134i
$512$	−1.00000			−0.0441942
$513$	−13.2771	−	21.9470i	−0.586199	−	0.968985i
$514$	9.56434	−	16.5659i	0.421865	−	0.730691i
$515$	−19.7106	+	16.5391i	−0.868551	+	0.728801i
$516$	5.16961	−	1.92162i	0.227580	−	0.0845944i
$517$	0.948343	+	0.795755i	0.0417081	+	0.0349972i
$518$	−3.30298	−	3.72794i	−0.145125	−	0.163796i
$519$	2.39067	+	4.07630i	0.104939	+	0.178930i
$520$	1.56024	+	0.567879i	0.0684209	+	0.0249032i
$521$	−2.88908			−0.126573			−0.0632863	−	0.997995i	$-0.520158\pi$
$521$	−2.88908			−0.126573			−0.0632863	+	0.997995i	$0.520158\pi$
$522$	−5.87247	+	10.4996i	−0.257031	+	0.459555i
$523$	18.5448			0.810910			0.405455	−	0.914115i	$-0.367113\pi$
$523$	18.5448			0.810910			0.405455	+	0.914115i	$0.367113\pi$
$524$	−2.83790	−	16.0945i	−0.123974	−	0.703092i
$525$	2.98025	+	1.58917i	0.130069	+	0.0693572i
$526$	9.22418	−	3.35733i	0.402193	−	0.146386i
$527$	36.3348	+	30.4885i	1.58277	+	1.32810i
$528$	−0.246785	−	1.34585i	−0.0107399	−	0.0585704i
$529$	15.8963	+	5.78578i	0.691144	+	0.251556i
$530$	22.1335			0.961418
$531$	19.8693	+	33.3554i	0.862252	+	1.44750i
$532$	4.79547	+	12.1484i	0.207910	+	0.526701i
$533$	−6.66771	+	5.59488i	−0.288811	+	0.242341i
$534$	−2.20435	+	3.87891i	−0.0953917	+	0.167857i
$535$	16.6581	+	13.9778i	0.720193	+	0.604313i
$536$	1.15716	−	0.421173i	0.0499818	−	0.0181919i
$537$	−2.82153	+	1.04880i	−0.121758	+	0.0452592i
$538$	0.997259	+	0.362972i	0.0429949	+	0.0156489i
$539$	−4.03887	+	3.77716i	−0.173966	+	0.162694i
$540$	2.41152	+	12.2100i	0.103775	+	0.525435i
$541$	17.2021	+	29.7950i	0.739577	+	1.28099i	0.952686	+	0.303957i	$0.0983078\pi$
$541$	17.2021	+	29.7950i	0.739577	+	1.28099i	−0.213109	+	0.977029i	$0.568359\pi$
$542$	−22.6671	+	19.0199i	−0.973633	+	0.816975i
$543$	11.3076	−	4.20318i	0.485255	−	0.180376i
$544$	1.42469	−	8.07981i	0.0610830	−	0.346419i
$545$	−7.73379	+	43.8605i	−0.331279	+	1.87878i
$546$	1.95872	−	2.50092i	0.0838255	−	0.107029i
$547$	0.956650	−	0.802725i	0.0409034	−	0.0343220i	−0.622107	−	0.782932i	$-0.713723\pi$
$547$	0.956650	−	0.802725i	0.0409034	−	0.0343220i	0.663010	+	0.748610i	$0.269279\pi$
$548$	0.520078	−	0.900801i	0.0222166	−	0.0384803i
$549$	−6.16549	−	5.03176i	−0.263137	−	0.214750i
$550$	0.291118	+	0.504231i	0.0124133	+	0.0215005i
$551$	15.1644	−	12.7244i	0.646024	−	0.542079i
$552$	0.770512	+	4.20200i	0.0327952	+	0.178849i
$553$	−17.2095	−	19.4237i	−0.731824	−	0.825982i
$554$	20.4393	−	7.43930i	0.868383	−	0.316066i
$555$	1.40860	+	7.68180i	0.0597916	+	0.326074i
$556$	9.78314	+	3.56077i	0.414897	+	0.151010i
$557$	−15.6185	−	27.0520i	−0.661775	−	1.14623i	−0.980149	−	0.198263i	$-0.936470\pi$
$557$	−15.6185	−	27.0520i	−0.661775	−	1.14623i	0.318374	−	0.947965i	$-0.396863\pi$
$558$	3.24440	+	17.0375i	0.137346	+	0.721255i
$559$	1.10365	+	1.91158i	0.0466795	+	0.0808513i
$560$	−0.170433	−	6.33484i	−0.00720211	−	0.267696i
$561$	11.2258	−	0.0765655i	0.473952	−	0.00323260i
$562$	−3.78251	+	1.37672i	−0.159555	+	0.0580734i
$563$	30.7025	−	11.1748i	1.29396	−	0.470962i	0.398934	−	0.916980i	$-0.369380\pi$
$563$	30.7025	−	11.1748i	1.29396	−	0.470962i	0.895024	+	0.446018i	$0.147158\pi$
$564$	−0.453089	+	2.67621i	−0.0190785	+	0.112689i
$565$	−5.28087	−	29.9493i	−0.222168	−	1.25998i
$566$	15.0311			0.631803
$567$	23.6395	+	2.85892i	0.992766	+	0.120063i
$568$	−6.65034			−0.279042
$569$	−0.639933	−	3.62924i	−0.0268274	−	0.152146i	0.968451	−	0.249202i	$-0.0801684\pi$
$569$	−0.639933	−	3.62924i	−0.0268274	−	0.152146i	−0.995279	+	0.0970565i	$0.969057\pi$
$570$	3.41859	−	20.1922i	0.143189	−	0.845758i
$571$	−37.1611	+	13.5255i	−1.55514	+	0.566026i	−0.969617	−	0.244628i	$-0.921334\pi$
$571$	−37.1611	+	13.5255i	−1.55514	+	0.566026i	−0.585526	+	0.810654i	$0.699112\pi$
$572$	0.514592	−	0.187296i	0.0215162	−	0.00783124i
$573$	−8.88660	+	0.0606112i	−0.371243	+	0.00253207i
$574$	29.2064	+	15.8307i	1.21905	+	0.660760i
$575$	−0.908928	−	1.57431i	−0.0379049	−	0.0656532i
$576$	2.27162	−	1.95953i	0.0946507	−	0.0816471i
$577$	0.149601	+	0.259116i	0.00622797	+	0.0107872i	0.869123	−	0.494597i	$-0.164684\pi$
$577$	0.149601	+	0.259116i	0.00622797	+	0.0107872i	−0.862895	+	0.505384i	$0.831351\pi$
$578$	47.2787	+	17.2081i	1.96654	+	0.715761i
$579$	4.86435	+	26.5278i	0.202155	+	1.10246i
$580$	−9.02576	+	3.28511i	−0.374774	+	0.136407i
$581$	−14.2652	+	2.91295i	−0.591820	+	0.120849i
$582$	−5.10603	−	27.8458i	−0.211652	−	1.15425i
$583$	5.59213	−	4.69235i	0.231602	−	0.194337i
$584$	−3.58620	−	6.21149i	−0.148398	−	0.257033i
$585$	−4.65703	+	1.76733i	−0.192545	+	0.0730699i
$586$	3.96203	−	6.86243i	0.163670	−	0.283484i
$587$	−2.75096	+	2.30833i	−0.113544	+	0.0952751i	−0.697792	−	0.716300i	$-0.745834\pi$
$587$	−2.75096	+	2.30833i	−0.113544	+	0.0952751i	0.584248	+	0.811575i	$0.301390\pi$
$588$	−11.6234	−	3.44898i	−0.479343	−	0.142233i
$589$	4.95571	−	28.1052i	0.204196	−	1.15806i
$590$	−5.38272	+	30.5269i	−0.221603	+	1.25677i
$591$	26.1019	−	9.70245i	1.07369	−	0.399105i
$592$	1.44210	−	1.21006i	0.0592698	−	0.0497333i
$593$	−13.3200	−	23.0710i	−0.546988	−	0.947411i	−0.998479	−	0.0551350i	$-0.982441\pi$
$593$	−13.3200	−	23.0710i	−0.546988	−	0.947411i	0.451491	−	0.892276i	$-0.350892\pi$
$594$	3.19783	+	2.57366i	0.131208	+	0.105599i
$595$	51.4270	+	7.64810i	2.10830	+	0.313541i
$596$	−16.8895	−	6.14726i	−0.691819	−	0.251801i
$597$	−29.7081	+	11.0429i	−1.21587	+	0.451956i
$598$	−1.60666	+	0.584776i	−0.0657011	+	0.0239133i
$599$	−23.8923	−	20.0480i	−0.976211	−	0.819138i	0.00730254	−	0.999973i	$-0.497676\pi$
$599$	−23.8923	−	20.0480i	−0.976211	−	0.819138i	−0.983513	+	0.180835i	$0.942120\pi$
$600$	−0.630728	+	1.10987i	−0.0257494	+	0.0453101i
$601$	26.4996	−	22.2358i	1.08094	−	0.907017i	0.0849418	−	0.996386i	$-0.472930\pi$
$601$	26.4996	−	22.2358i	1.08094	−	0.907017i	0.995999	+	0.0893692i	$0.0284851\pi$
$602$	5.23971	−	6.59694i	0.213555	−	0.268871i
$603$	−1.80333	+	3.22424i	−0.0734372	+	0.131301i
$604$	5.78847			0.235530
$605$	−23.3537	−	8.50006i	−0.949464	−	0.345577i
$606$	−2.19762	−	11.9848i	−0.0892722	−	0.486847i
$607$	−25.6068	−	21.4866i	−1.03935	−	0.872115i	−0.0474128	−	0.998875i	$-0.515098\pi$
$607$	−25.6068	−	21.4866i	−1.03935	−	0.872115i	−0.991933	+	0.126760i	$0.959542\pi$
$608$	−4.63876	+	1.68837i	−0.188126	+	0.0684724i
$609$	0.619504	+	18.3661i	0.0251036	+	0.744233i
$610$	−1.10332	−	6.25727i	−0.0446723	−	0.253349i
$611$	−1.08632			−0.0439477
$612$	12.5963	+	21.1459i	0.509175	+	0.854774i
$613$	33.5179			1.35377			0.676887	−	0.736087i	$-0.263328\pi$
$613$	33.5179			1.35377			0.676887	+	0.736087i	$0.263328\pi$
$614$	−19.7156	−	7.17589i	−0.795657	−	0.289595i
$615$	−26.3528	−	44.9338i	−1.06265	−	1.81191i
$616$	−1.38606	−	1.56439i	−0.0558459	−	0.0630311i
$617$	−18.8941	−	15.8540i	−0.760648	−	0.638259i	0.177648	−	0.984094i	$-0.443151\pi$
$617$	−18.8941	−	15.8540i	−0.760648	−	0.638259i	−0.938295	+	0.345835i	$0.887596\pi$
$618$	−17.4405	+	6.48286i	−0.701559	+	0.260779i
$619$	9.01138	−	7.56145i	0.362198	−	0.303920i	−0.443468	−	0.896290i	$-0.646252\pi$
$619$	9.01138	−	7.56145i	0.362198	−	0.303920i	0.805666	+	0.592370i	$0.201808\pi$
$620$	−6.92362	+	11.9921i	−0.278059	+	0.481612i
$621$	−9.98426	−	8.03549i	−0.400654	−	0.322453i
$622$	−8.78249			−0.352146
$623$	0.183287	+	6.81261i	0.00734324	+	0.272941i
$624$	0.925005	+	0.765481i	0.0370298	+	0.0306438i
$625$	−4.88679	+	27.7144i	−0.195472	+	1.10858i
$626$	23.8274	+	19.9935i	0.952333	+	0.799102i
$627$	−3.41706	−	5.82639i	−0.136464	−	0.232684i
$628$	−10.4395	−	3.79967i	−0.416582	−	0.151623i
$629$	7.72253	+	13.3758i	0.307917	+	0.533329i
$630$	12.8005	+	14.0563i	0.509983	+	0.560018i
$631$	10.3809	−	17.9802i	0.413256	−	0.715780i	−0.581988	−	0.813198i	$-0.697725\pi$
$631$	10.3809	−	17.9802i	0.413256	−	0.715780i	0.995244	+	0.0974173i	$0.0310582\pi$
$632$	7.51377	−	6.30480i	0.298882	−	0.250791i
$633$	−21.8045	−	7.76819i	−0.866651	−	0.308758i
$634$	−3.62006	+	20.5304i	−0.143771	+	0.815365i
$635$	−4.55379	−	3.82108i	−0.180712	−	0.151635i
$636$	15.0772	+	5.37147i	0.597849	+	0.212993i
$637$	0.584448	−	4.81710i	0.0231567	−	0.190861i
$638$	−1.58395	+	2.74348i	−0.0627091	+	0.108615i
$639$	15.1070	−	13.0315i	0.597624	−	0.515520i
$640$	2.39521			0.0946789
$641$	−2.43434	−	13.8059i	−0.0961508	−	0.545298i	−0.994389	−	0.105789i	$-0.966263\pi$
$641$	−2.43434	−	13.8059i	−0.0961508	−	0.545298i	0.898238	−	0.439510i	$-0.144848\pi$
$642$	7.95517	+	13.5643i	0.313965	+	0.535338i
$643$	0.443611	−	2.51585i	0.0174943	−	0.0992153i	−0.974810	−	0.223035i	$-0.928403\pi$
$643$	0.443611	−	2.51585i	0.0174943	−	0.0992153i	0.992305	+	0.123820i	$0.0395146\pi$
$644$	4.32755	+	4.88434i	0.170529	+	0.192470i
$645$	−12.3823	+	4.60267i	−0.487553	+	0.181230i
$646$	−7.03292	−	39.8857i	−0.276706	−	1.56928i
$647$	20.8786	−	36.1629i	0.820824	−	1.42171i	−0.0842457	−	0.996445i	$-0.526848\pi$
$647$	20.8786	−	36.1629i	0.820824	−	1.42171i	0.905070	−	0.425264i	$-0.139819\pi$
$648$	−1.32048	+	8.90260i	−0.0518733	+	0.349727i
$649$	5.11181	+	8.85391i	0.200656	+	0.347546i
$650$	−0.480098	−	0.174741i	−0.0188310	−	0.00685392i
$651$	17.7038	+	19.7091i	0.693866	+	0.772461i
$652$	−1.47061	−	1.23399i	−0.0575935	−	0.0483267i
$653$	13.5093	−	4.91697i	0.528658	−	0.192416i	−0.0638811	−	0.997958i	$-0.520348\pi$
$653$	13.5093	−	4.91697i	0.528658	−	0.192416i	0.592539	+	0.805542i	$0.298126\pi$
$654$	−15.9125	+	28.0006i	−0.622228	+	1.09491i
$655$	6.79736	+	38.5497i	0.265595	+	1.50626i
$656$	−6.27815	+	10.8741i	−0.245121	+	0.424562i
$657$	20.3181	+	7.08284i	0.792684	+	0.276328i
$658$	1.52234	+	3.85656i	0.0593468	+	0.150344i
$659$	−4.21479	−	23.9033i	−0.164185	−	0.931140i	−0.949901	−	0.312552i	$-0.898816\pi$
$659$	−4.21479	−	23.9033i	−0.164185	−	0.931140i	0.785716	−	0.618588i	$-0.212295\pi$
$660$	0.591102	+	3.22358i	0.0230086	+	0.125478i
$661$	0.364000	−	2.06434i	0.0141579	−	0.0802937i	−0.976910	−	0.213651i	$-0.931465\pi$
$661$	0.364000	−	2.06434i	0.0141579	−	0.0802937i	0.991068	+	0.133357i	$0.0425757\pi$
$662$	0.100583	−	0.570434i	0.00390926	−	0.0221705i
$663$	−7.50278	+	6.38329i	−0.291384	+	0.247906i
$664$	−0.955586	−	5.41940i	−0.0370839	−	0.210313i
$665$	−11.4861	−	29.0980i	−0.445414	−	1.12837i
$666$	−0.904734	+	5.57463i	−0.0350577	+	0.216012i
$667$	4.94540	−	8.56568i	0.191487	−	0.331664i
$668$	3.45177	+	19.5759i	0.133553	+	0.757416i
$669$	14.7900	+	25.2183i	0.571815	+	0.974995i
$670$	−2.77165	+	1.00880i	−0.107078	+	0.0389732i
$671$	−1.60531	−	1.34702i	−0.0619724	−	0.0520010i
$672$	1.42127	−	4.35660i	0.0548268	−	0.168060i
$673$	−29.9005	−	10.8829i	−1.15258	−	0.419505i	−0.306139	−	0.951987i	$-0.599037\pi$
$673$	−29.9005	−	10.8829i	−1.15258	−	0.419505i	−0.846442	+	0.532482i	$0.821260\pi$
$674$	−2.48122	−	4.29759i	−0.0955729	−	0.165537i
$675$	−0.742046	−	3.75712i	−0.0285614	−	0.144612i
$676$	6.25973	−	10.8422i	0.240759	−	0.417007i
$677$	−3.90751	−	22.1606i	−0.150178	−	0.851700i	−0.963063	−	0.269276i	$-0.913215\pi$
$677$	−3.90751	−	22.1606i	−0.150178	−	0.851700i	0.812885	−	0.582424i	$-0.197896\pi$
$678$	3.67096	−	21.6828i	0.140982	−	0.832723i
$679$	−28.6778	−	32.3675i	−1.10055	−	1.24215i
$680$	−3.41242	+	19.3528i	−0.130861	+	0.742147i
$681$	11.7599	−	20.6934i	0.450639	−	0.792972i
$682$	0.793060	+	4.49766i	0.0303678	+	0.172224i
$683$	26.1748			1.00155			0.500775	−	0.865578i	$-0.333048\pi$
$683$	26.1748			1.00155			0.500775	+	0.865578i	$0.333048\pi$
$684$	7.22906	−	12.9251i	0.276410	−	0.494204i
$685$	−1.24569	+	2.15761i	−0.0475955	+	0.0824379i
$686$	−17.9203	+	4.67570i	−0.684201	+	0.178519i
$687$	−15.0278	+	12.7855i	−0.573347	+	0.487797i
$688$	2.43924	+	2.04677i	0.0929953	+	0.0780323i
$689$	−1.11234	+	6.30840i	−0.0423768	+	0.240331i
$690$	−1.84554	−	10.0647i	−0.0702584	−	0.383155i
$691$	−25.8163	+	21.6624i	−0.982097	+	0.824077i	−0.984404	−	0.175920i	$-0.943710\pi$
$691$	−25.8163	+	21.6624i	−0.982097	+	0.824077i	0.00230755	+	0.999997i	$0.499265\pi$
$692$	−1.36417	+	2.36281i	−0.0518580	+	0.0898207i
$693$	6.21407	+	0.837670i	0.236053	+	0.0318204i
$694$	−10.6227	−	18.3991i	−0.403233	−	0.698420i
$695$	−23.4327	−	8.52879i	−0.888851	−	0.323515i
$696$	−6.94553	+	0.0473721i	−0.263269	+	0.00179563i
$697$	−78.9161	−	66.2184i	−2.98916	−	2.50820i
$698$	2.10375	−	11.9310i	0.0796283	−	0.451594i
$699$	−0.905895	+	5.35074i	−0.0342641	+	0.202383i
$700$	0.0524437	+	1.94928i	0.00198219	+	0.0736759i
$701$	3.32754			0.125680			0.0628398	−	0.998024i	$-0.479984\pi$
$701$	3.32754			0.125680			0.0628398	+	0.998024i	$0.479984\pi$
$702$	−3.60124	+	0.0736961i	−0.135920	+	0.00278148i
$703$	4.64650	−	8.04798i	0.175246	−	0.303535i
$704$	0.605160	−	0.507789i	0.0228078	−	0.0191380i
$705$	1.08524	−	6.41007i	0.0408726	−	0.241417i
$706$	−18.6772	−	15.6721i	−0.702927	−	0.589826i
$707$	−12.3428	−	13.9309i	−0.464201	−	0.523925i
$708$	−11.0751	+	19.4884i	−0.416228	+	0.732419i
$709$	−16.9602	−	6.17301i	−0.636954	−	0.231832i	0.00330105	−	0.999995i	$-0.498949\pi$
$709$	−16.9602	−	6.17301i	−0.636954	−	0.231832i	−0.640255	+	0.768162i	$0.721171\pi$
$710$	15.9290			0.597803
$711$	−4.71394	+	29.0455i	−0.176787	+	1.08929i
$712$	−2.57586			−0.0965343
$713$	−2.47609	−	14.0426i	−0.0927303	−	0.525900i
$714$	33.1756	+	17.6904i	1.24157	+	0.662047i
$715$	−1.23255	+	0.448613i	−0.0460949	+	0.0167772i
$716$	−1.33132	−	1.11711i	−0.0497538	−	0.0417484i
$717$	8.20175	−	6.97796i	0.306300	−	0.260597i
$718$	4.90135	+	1.78395i	0.182917	+	0.0665763i
$719$	21.6442			0.807192			0.403596	−	0.914937i	$-0.367760\pi$
$719$	21.6442			0.807192			0.403596	+	0.914937i	$0.367760\pi$
$720$	−5.44099	+	4.69349i	−0.202774	+	0.174916i
$721$	−17.6770	+	22.2558i	−0.658325	+	0.828848i
$722$	−4.11264	+	3.45092i	−0.153057	+	0.128430i
$723$	23.0357	+	39.2778i	0.856706	+	1.46076i
$724$	5.33540	+	4.47693i	0.198288	+	0.166384i
$725$	2.77730	−	1.01086i	0.103146	−	0.0375422i
$726$	−13.8455	−	11.4578i	−0.513856	−	0.425238i
$727$	18.2669	+	6.64862i	0.677483	+	0.246584i	0.657766	−	0.753222i	$-0.271501\pi$
$727$	18.2669	+	6.64862i	0.677483	+	0.246584i	0.0197166	+	0.999806i	$0.493724\pi$
$728$	1.81409	+	0.269787i	0.0672348	+	0.00999898i
$729$	−14.4453	−	22.8108i	−0.535011	−	0.844845i
$730$	8.58971	+	14.8778i	0.317919	+	0.550652i
$731$	−20.0126	+	16.7926i	−0.740195	+	0.621097i
$732$	0.766969	−	4.53016i	0.0283480	−	0.167440i
$733$	−5.33398	+	30.2505i	−0.197015	+	1.11733i	0.712504	+	0.701668i	$0.247561\pi$
$733$	−5.33398	+	30.2505i	−0.197015	+	1.11733i	−0.909520	+	0.415661i	$0.863550\pi$
$734$	−6.48424	+	36.7740i	−0.239338	+	1.35735i
$735$	27.8406	+	8.26102i	1.02692	+	0.304712i
$736$	−1.88943	+	1.58542i	−0.0696453	+	0.0584393i
$737$	−0.486401	+	0.842471i	−0.0179168	+	0.0310328i
$738$	−7.04655	−	37.0040i	−0.259387	−	1.36214i
$739$	−13.6817	−	23.6975i	−0.503291	−	0.871725i	−0.999993	−	0.00380388i	$-0.998789\pi$
$739$	−13.6817	−	23.6975i	−0.503291	−	0.871725i	0.496702	−	0.867921i	$-0.334544\pi$
$740$	−3.45412	+	2.89835i	−0.126976	+	0.106546i
$741$	5.58329	+	1.98913i	0.205107	+	0.0730726i
$742$	23.9544	−	4.89148i	0.879393	−	0.179572i
$743$	−14.5217	+	5.28547i	−0.532750	+	0.193905i	−0.594366	−	0.804195i	$-0.702597\pi$
$743$	−14.5217	+	5.28547i	−0.532750	+	0.193905i	0.0616160	+	0.998100i	$0.480375\pi$
$744$	−7.62661	+	6.48864i	−0.279605	+	0.237885i
$745$	40.4538	+	14.7240i	1.48211	+	0.539444i
$746$	−6.04944	−	10.4779i	−0.221486	−	0.383625i
$747$	12.7902	+	10.4383i	0.467969	+	0.381917i
$748$	3.24067	+	5.61301i	0.118491	+	0.205232i
$749$	21.1176	+	11.4463i	0.771621	+	0.418239i
$750$	−8.73807	+	15.3760i	−0.319069	+	0.561453i
$751$	9.51469	−	3.46306i	0.347196	−	0.126369i	−0.162535	−	0.986703i	$-0.551967\pi$
$751$	9.51469	−	3.46306i	0.347196	−	0.126369i	0.509731	+	0.860334i	$0.329745\pi$
$752$	−1.47259	+	0.535978i	−0.0536998	+	0.0195451i
$753$	−46.2174	+	17.1796i	−1.68426	+	0.626061i
$754$	−0.482709	−	2.73758i	−0.0175792	−	0.0996968i
$755$	−13.8646			−0.504585
$756$	5.30831	+	12.6816i	0.193061	+	0.461224i
$757$	20.9252			0.760538			0.380269	−	0.924876i	$-0.375831\pi$
$757$	20.9252			0.760538			0.380269	+	0.924876i	$0.375831\pi$
$758$	0.580255	+	3.29079i	0.0210758	+	0.119527i
$759$	−2.60001	−	2.15162i	−0.0943745	−	0.0780990i
$760$	11.1108	−	4.04400i	0.403031	−	0.146691i
$761$	16.1387	−	5.87400i	0.585027	−	0.212932i	−0.0325140	−	0.999471i	$-0.510351\pi$
$761$	16.1387	−	5.87400i	0.585027	−	0.212932i	0.617541	+	0.786539i	$0.288129\pi$
$762$	−2.17469	−	3.70803i	−0.0787806	−	0.134328i
$763$	1.32309	+	49.1780i	0.0478991	+	1.78036i
$764$	−2.56540	−	4.44340i	−0.0928129	−	0.160757i
$765$	−30.1707	−	50.6489i	−1.09083	−	1.83122i
$766$	0.986429	+	1.70855i	0.0356411	+	0.0617322i
$767$	−8.43015	−	3.06832i	−0.304395	−	0.110791i
$768$	1.63160	+	0.581282i	0.0588752	+	0.0209752i
$769$	44.6936	−	16.2671i	1.61169	−	0.586608i	0.629918	−	0.776662i	$-0.283088\pi$
$769$	44.6936	−	16.2671i	1.61169	−	0.586608i	0.981774	+	0.190054i	$0.0608662\pi$
$770$	3.31990	+	3.74704i	0.119641	+	0.135034i
$771$	−25.2346	+	21.4693i	−0.908803	+	0.773200i
$772$	−11.9282	+	10.0090i	−0.429306	+	0.360230i
$773$	19.9622	+	34.5756i	0.717992	+	1.24360i	0.961794	+	0.273773i	$0.0882718\pi$
$773$	19.9622	+	34.5756i	0.717992	+	1.24360i	−0.243803	+	0.969825i	$0.578395\pi$
$774$	−9.55173	+	0.130302i	−0.343330	+	0.00468359i
$775$	2.13045	−	3.69006i	0.0765282	−	0.132551i
$776$	12.5209	−	10.5063i	0.449473	−	0.377153i
$777$	3.22215	+	8.00247i	0.115594	+	0.287087i
$778$	−1.52962	+	8.67489i	−0.0548395	+	0.311010i
$779$	−10.7634	+	61.0421i	−0.385638	+	2.18706i
$780$	−2.21558	−	1.83349i	−0.0793305	−	0.0656494i
$781$	4.02452	−	3.37697i	0.144009	−	0.120838i
$782$	−10.1180	−	17.5249i	−0.361820	−	0.626691i
$783$	15.6847	−	13.7176i	0.560527	−	0.490226i
$784$	−1.58445	−	6.81832i	−0.0565873	−	0.243512i
$785$	25.0048	+	9.10100i	0.892459	+	0.324829i
$786$	−4.72514	+	27.9094i	−0.168540	+	0.995495i
$787$	0.431652	−	0.157108i	0.0153867	−	0.00560031i	−0.334315	−	0.942461i	$-0.608505\pi$
$787$	0.431652	−	0.157108i	0.0153867	−	0.00560031i	0.349702	+	0.936861i	$0.386283\pi$
$788$	12.3160	+	10.3344i	0.438740	+	0.368146i
$789$	−17.0017	+	0.115960i	−0.605277	+	0.00412830i
$790$	−17.9970	+	15.1013i	−0.640306	+	0.537281i
$791$	−12.3341	−	31.2461i	−0.438549	−	1.11098i
$792$	−0.379662	+	2.33933i	−0.0134907	+	0.0831245i
$793$	1.83887			0.0653002
$794$	−29.2921	−	10.6615i	−1.03954	−	0.378361i
$795$	−36.1130	−	12.8658i	−1.28080	−	0.456303i
$796$	−14.0176	−	11.7621i	−0.496839	−	0.416897i
$797$	−30.5597	+	11.1228i	−1.08248	+	0.393991i	−0.820831	−	0.571172i	$-0.806489\pi$
$797$	−30.5597	+	11.1228i	−1.08248	+	0.393991i	−0.261651	+	0.965163i	$0.584267\pi$
$798$	−0.762615	−	22.6089i	−0.0269963	−	0.800345i
$799$	−2.23262	−	12.6618i	−0.0789845	−	0.447943i
$800$	−0.737026			−0.0260578
$801$	5.85136	−	5.04747i	0.206747	−	0.178344i
$802$	14.6022			0.515622
$803$	5.32435	+	1.93791i	0.187892	+	0.0683872i
$804$	−2.13284	+	0.0145471i	−0.0752196	+	0.000513037i
$805$	−10.3654	−	11.6990i	−0.365332	−	0.412336i
$806$	−3.06997	−	2.57601i	−0.108135	−	0.0907362i
$807$	−1.41614	−	1.17191i	−0.0498503	−	0.0412533i
$808$	5.38894	−	4.52186i	0.189582	−	0.159079i
$809$	−4.70851	+	8.15538i	−0.165542	+	0.286728i	−0.936848	−	0.349737i	$-0.886271\pi$
$809$	−4.70851	+	8.15538i	−0.165542	+	0.286728i	0.771305	+	0.636465i	$0.219604\pi$
$810$	3.16282	−	21.3236i	0.111130	−	0.749235i
$811$	26.8671			0.943432			0.471716	−	0.881751i	$-0.343635\pi$
$811$	26.8671			0.943432			0.471716	+	0.881751i	$0.343635\pi$
$812$	−9.04229	+	5.55005i	−0.317322	+	0.194769i
$813$	48.0395	−	17.8569i	1.68482	−	0.626269i
$814$	−0.258242	+	1.46456i	−0.00905137	+	0.0513329i
$815$	3.52242	+	2.95566i	0.123385	+	0.103532i
$816$	−7.02116	+	12.3548i	−0.245790	+	0.432506i
$817$	14.7708	+	5.37612i	0.516764	+	0.188087i
$818$	1.22112	+	2.11503i	0.0426953	+	0.0739504i
$819$	−4.64958	+	2.94192i	−0.162469	+	0.102799i
$820$	15.0375	−	26.0457i	0.525132	−	0.909555i
$821$	−23.9241	+	20.0747i	−0.834957	+	0.700612i	−0.956423	−	0.291984i	$-0.905685\pi$
$821$	−23.9241	+	20.0747i	−0.834957	+	0.700612i	0.121466	+	0.992596i	$0.461240\pi$
$822$	−1.37218	+	1.16743i	−0.0478601	+	0.0407189i
$823$	−6.19086	+	35.1101i	−0.215800	+	1.22386i	0.663714	+	0.747987i	$0.268979\pi$
$823$	−6.19086	+	35.1101i	−0.215800	+	1.22386i	−0.879513	+	0.475874i	$0.842132\pi$
$824$	−8.22916	−	6.90509i	−0.286676	−	0.240550i
$825$	−0.181887	−	0.991924i	−0.00633250	−	0.0345343i
$826$	0.920871	+	34.2279i	0.0320412	+	1.19094i
$827$	23.7610	−	41.1553i	0.826252	−	1.43111i	−0.0747067	−	0.997206i	$-0.523802\pi$
$827$	23.7610	−	41.1553i	0.826252	−	1.43111i	0.900959	−	0.433905i	$-0.142865\pi$
$828$	1.18538	−	7.30386i	0.0411948	−	0.253827i
$829$	26.7652			0.929594			0.464797	−	0.885417i	$-0.346127\pi$
$829$	26.7652			0.929594			0.464797	+	0.885417i	$0.346127\pi$
$830$	2.28883	+	12.9806i	0.0794464	+	0.450563i
$831$	−37.6731	+	0.256950i	−1.30686	+	0.00891349i
$832$	−0.120374	+	0.682673i	−0.00417320	+	0.0236674i
$833$	57.3481	−	3.08803i	1.98699	−	0.106994i
$834$	−13.8923	−	11.4965i	−0.481052	−	0.398091i
$835$	−8.26770	−	46.8885i	−0.286116	−	1.62264i
$836$	1.94985	−	3.37725i	0.0674371	−	0.116804i
$837$	4.61004	−	29.6843i	0.159346	−	1.02604i
$838$	5.83736	+	10.1106i	0.201648	+	0.349265i
$839$	−1.66593	−	0.606349i	−0.0575143	−	0.0209335i	0.313103	−	0.949719i	$-0.398632\pi$
$839$	−1.66593	−	0.606349i	−0.0575143	−	0.0209335i	−0.370617	+	0.928786i	$0.620854\pi$
$840$	−3.40425	+	10.4350i	−0.117458	+	0.360041i
$841$	−9.89664	−	8.30427i	−0.341263	−	0.286354i
$842$	23.7446	−	8.64232i	0.818292	−	0.297834i
$843$	6.97179	−	0.0475512i	0.240121	−	0.00163775i
$844$	−2.32062	−	13.1609i	−0.0798789	−	0.453016i
$845$	−14.9934	+	25.9693i	−0.515788	+	0.893370i
$846$	2.29489	−	4.10312i	0.0788999	−	0.141068i
$847$	−27.1535	−	4.03820i	−0.933005	−	0.138754i
$848$	1.60464	+	9.10035i	0.0551035	+	0.312507i
$849$	−24.5247	−	8.73728i	−0.841684	−	0.299863i
$850$	1.05003	−	5.95503i	0.0360158	−	0.204256i
$851$	0.806282	−	4.57265i	0.0276390	−	0.156749i
$852$	10.8507	+	3.86572i	0.371738	+	0.132437i
$853$	3.29825	+	18.7053i	0.112930	+	0.640457i	0.987754	+	0.156017i	$0.0498654\pi$
$853$	3.29825	+	18.7053i	0.112930	+	0.640457i	−0.874825	+	0.484440i	$0.839023\pi$
$854$	−2.57694	−	6.52821i	−0.0881811	−	0.223391i
$855$	−17.3151	+	30.9584i	−0.592165	+	1.05875i
$856$	−4.53940	+	7.86247i	−0.155153	+	0.268734i
$857$	7.81173	+	44.3025i	0.266844	+	1.51335i	0.763734	+	0.645532i	$0.223364\pi$
$857$	7.81173	+	44.3025i	0.266844	+	1.51335i	−0.496890	+	0.867813i	$0.665525\pi$
$858$	−0.948479	+	0.00646912i	−0.0323805	+	0.000220852i
$859$	6.19493	−	2.25477i	0.211368	−	0.0769317i	−0.234166	−	0.972197i	$-0.575236\pi$
$859$	6.19493	−	2.25477i	0.211368	−	0.0769317i	0.445534	+	0.895265i	$0.353014\pi$
$860$	−5.84250	−	4.90244i	−0.199228	−	0.167172i
$861$	−38.4511	−	42.8065i	−1.31041	−	1.45884i
$862$	23.4278	+	8.52703i	0.797955	+	0.290432i
$863$	−1.20668	−	2.09002i	−0.0410757	−	0.0711453i	0.844757	−	0.535151i	$-0.179745\pi$
$863$	−1.20668	−	2.09002i	−0.0410757	−	0.0711453i	−0.885832	+	0.464005i	$0.846412\pi$
$864$	−4.84540	+	1.87672i	−0.164844	+	0.0638472i
$865$	3.26747	−	5.65943i	0.111097	−	0.192426i
$866$	4.67757	+	26.5278i	0.158950	+	0.901453i
$867$	−67.1372	−	55.5589i	−2.28010	−	1.88688i
$868$	−4.84298	+	14.5087i	−0.164381	+	0.492458i
$869$	−1.34552	+	7.63082i	−0.0456436	+	0.258858i
$870$	16.6360	−	0.113466i	0.564013	−	0.00384686i
$871$	−0.148231	−	0.840661i	−0.00502262	−	0.0284847i
$872$	−18.5943			−0.629681
$873$	−7.85527	+	48.4012i	−0.265861	+	1.63813i
$874$	−6.08783	+	10.5444i	−0.205924	+	0.356671i
$875$	0.726552	+	27.0052i	0.0245619	+	0.912944i
$876$	2.24062	+	12.2192i	0.0757035	+	0.412850i
$877$	−19.5251	−	16.3835i	−0.659317	−	0.553233i	0.250565	−	0.968100i	$-0.419384\pi$
$877$	−19.5251	−	16.3835i	−0.659317	−	0.553233i	−0.909882	+	0.414867i	$0.863828\pi$
$878$	3.43336	−	19.4716i	0.115870	−	0.657134i
$879$	−10.4534	+	8.89367i	−0.352586	+	0.299976i
$880$	−1.44948	+	1.21626i	−0.0488621	+	0.0410002i
$881$	4.71552	−	8.16752i	0.158870	−	0.275171i	−0.775592	−	0.631235i	$-0.782548\pi$
$881$	4.71552	−	8.16752i	0.158870	−	0.275171i	0.934461	+	0.356064i	$0.115882\pi$
$882$	16.9600	+	12.3838i	0.571072	+	0.416986i
$883$	20.6509	+	35.7685i	0.694959	+	1.20370i	0.970194	+	0.242328i	$0.0779110\pi$
$883$	20.6509	+	35.7685i	0.694959	+	1.20370i	−0.275235	+	0.961377i	$0.588756\pi$
$884$	−5.34437	−	1.94519i	−0.179750	−	0.0654238i
$885$	26.5272	−	46.6788i	0.891702	−	1.56909i
$886$	−9.65486	−	8.10139i	−0.324361	−	0.272172i
$887$	5.07854	−	28.8018i	0.170521	−	0.967070i	−0.772667	−	0.634811i	$-0.781078\pi$
$887$	5.07854	−	28.8018i	0.170521	−	0.967070i	0.943188	−	0.332259i	$-0.107811\pi$
$888$	−3.05631	+	1.13607i	−0.102563	+	0.0381240i
$889$	−5.77288	−	3.12905i	−0.193616	−	0.104945i
$890$	6.16971			0.206809
$891$	−3.72155	−	6.05802i	−0.124677	−	0.202951i
$892$	−8.43952	+	14.6177i	−0.282576	+	0.489436i
$893$	−5.92605	+	4.97255i	−0.198308	+	0.166400i
$894$	23.9835	+	19.8474i	0.802128	+	0.663796i
$895$	3.18879	+	2.67571i	0.106589	+	0.0894392i
$896$	2.59226	−	0.529339i	0.0866013	−	0.0176840i
$897$	2.96134	−	0.0201979i	0.0988762	−	0.000674387i
$898$	1.81885	+	0.662006i	0.0606957	+	0.0220914i
$899$	23.1832			0.773204
$900$	1.67424	−	1.44423i	0.0558080	−	0.0481408i
$901$	−75.8152			−2.52577
$902$	−1.72246	−	9.76854i	−0.0573515	−	0.325257i
$903$	−12.3838	+	7.71780i	−0.412107	+	0.256832i
$904$	11.9310	−	4.34253i	0.396820	−	0.144431i
$905$	−12.7794	−	10.7232i	−0.424801	−	0.356451i
$906$	−9.44446	−	3.36473i	−0.313771	−	0.111786i
$907$	−22.7403	−	8.27679i	−0.755079	−	0.274826i	−0.0643375	−	0.997928i	$-0.520493\pi$
$907$	−22.7403	−	8.27679i	−0.755079	−	0.274826i	−0.690741	+	0.723102i	$0.742716\pi$
$908$	13.7418			0.456037
$909$	−3.38088	+	20.8317i	−0.112137	+	0.690945i
$910$	−4.34513	−	0.646197i	−0.144040	−	0.0214212i
$911$	−37.5102	+	31.4748i	−1.24277	+	1.04281i	−0.245467	+	0.969405i	$0.578941\pi$
$911$	−37.5102	+	31.4748i	−1.24277	+	1.04281i	−0.997302	+	0.0734022i	$0.976614\pi$
$912$	8.55001	−	0.0583155i	0.283119	−	0.00193102i
$913$	3.33019	+	2.79436i	0.110213	+	0.0924799i
$914$	11.6160	−	4.22789i	0.384225	−	0.139846i
$915$	−1.83705	+	10.8507i	−0.0607311	+	0.358713i
$916$	−10.7046	−	3.89615i	−0.353689	−	0.128732i
$917$	15.8760	+	40.2189i	0.524272	+	1.32815i
$918$	−8.26033	−	41.8236i	−0.272631	−	1.38039i
$919$	6.10206	+	10.5691i	0.201288	+	0.348642i	0.948944	−	0.315445i	$-0.102154\pi$
$919$	6.10206	+	10.5691i	0.201288	+	0.348642i	−0.747655	+	0.664087i	$0.768821\pi$
$920$	4.52558	−	3.79741i	0.149204	−	0.125197i
$921$	27.9967	+	23.1685i	0.922523	+	0.763427i
$922$	−5.82845	+	33.0548i	−0.191950	+	1.08860i
$923$	−0.800525	+	4.54000i	−0.0263496	+	0.149436i
$924$	1.35214	+	3.35815i	0.0444821	+	0.110475i
$925$	1.06286	−	0.891847i	0.0349467	−	0.0293238i
$926$	1.24461	−	2.15572i	0.0409003	−	0.0708414i
$927$	32.2242	−	0.439592i	1.05838	−	0.0144381i
$928$	−2.00505	−	3.47284i	−0.0658189	−	0.114002i
$929$	−3.04389	+	2.55413i	−0.0998669	+	0.0837983i	−0.691354	−	0.722516i	$-0.742985\pi$
$929$	−3.04389	+	2.55413i	−0.0998669	+	0.0837983i	0.591487	+	0.806314i	$0.298541\pi$
$930$	18.2673	−	15.5416i	0.599009	−	0.509630i
$931$	−18.8617	−	28.9534i	−0.618168	−	0.948910i
$932$	−2.94425	+	1.07162i	−0.0964423	+	0.0351021i
$933$	14.3295	+	5.10510i	0.469126	+	0.167133i
$934$	−8.85464	−	3.22283i	−0.289733	−	0.105454i
$935$	−7.76209	−	13.4443i	−0.253848	−	0.439677i
$936$	−1.06428	−	1.78665i	−0.0347869	−	0.0583983i
$937$	−18.4462	−	31.9497i	−0.602611	−	1.04375i	−0.992424	−	0.122858i	$-0.960794\pi$
$937$	−18.4462	−	31.9497i	−0.602611	−	1.04375i	0.389814	−	0.920894i	$-0.372539\pi$
$938$	−2.77672	+	1.70432i	−0.0906631	+	0.0556480i
$939$	−27.2548	−	46.4718i	−0.889427	−	1.51655i
$940$	3.52716	−	1.28378i	0.115043	−	0.0418723i
$941$	−9.31016	+	3.38862i	−0.303503	+	0.110466i	−0.489282	−	0.872126i	$-0.662741\pi$
$941$	−9.31016	+	3.38862i	−0.303503	+	0.110466i	0.185780	+	0.982591i	$0.440519\pi$
$942$	14.8244	+	12.2678i	0.483005	+	0.399707i
$943$	5.37785	+	30.4993i	0.175127	+	0.993194i
$944$	−12.9416			−0.421214
$945$	−12.7145	−	30.3750i	−0.413603	−	0.988098i
$946$	−2.51546			−0.0817846
$947$	4.61678	+	26.1831i	0.150025	+	0.850836i	0.963194	+	0.268807i	$0.0866295\pi$
$947$	4.61678	+	26.1831i	0.150025	+	0.850836i	−0.813169	+	0.582028i	$0.802259\pi$
$948$	−15.9243	+	5.91928i	−0.517198	+	0.192249i
$949$	−4.67210	+	1.70050i	−0.151663	+	0.0552007i
$950$	−3.41889	+	1.24437i	−0.110923	+	0.0403728i
$951$	17.8404	−	31.3930i	0.578515	−	1.01799i
$952$	0.583794	+	21.6991i	0.0189209	+	0.703271i
$953$	11.6545	+	20.1861i	0.377525	+	0.653893i	0.990702	−	0.136053i	$-0.0434418\pi$
$953$	11.6545	+	20.1861i	0.377525	+	0.653893i	−0.613176	+	0.789946i	$0.710108\pi$
$954$	−21.4775	−	17.5282i	−0.695361	−	0.567496i
$955$	6.14467	+	10.6429i	0.198837	+	0.344395i
$956$	5.84226	+	2.12641i	0.188952	+	0.0687730i
$957$	4.17910	−	3.55553i	0.135091	−	0.114934i
$958$	−16.8049	+	6.11650i	−0.542943	+	0.197615i
$959$	−0.871347	+	2.61040i	−0.0281372	+	0.0842944i
$960$	−3.90802	−	1.39229i	−0.126131	−	0.0449360i
$961$	1.85575	−	1.55716i	0.0598628	−	0.0502309i
$962$	−0.652486	−	1.13014i	−0.0210370	−	0.0364371i
$963$	−5.09498	−	26.7556i	−0.164183	−	0.862187i
$964$	−13.1447	+	22.7673i	−0.423362	+	0.733284i
$965$	28.5706	−	23.9736i	0.919719	−	0.771736i
$966$	−4.22165	−	10.4848i	−0.135829	−	0.337343i
$967$	−7.56532	+	42.9051i	−0.243284	+	1.37973i	0.581159	+	0.813790i	$0.302599\pi$
$967$	−7.56532	+	42.9051i	−0.243284	+	1.37973i	−0.824444	+	0.565944i	$0.808512\pi$
$968$	1.80176	−	10.2183i	0.0579108	−	0.328429i
$969$	−11.7099	+	69.1655i	−0.376177	+	2.22191i
$970$	−29.9901	+	25.1647i	−0.962924	+	0.807989i
$971$	5.44733	+	9.43506i	0.174813	+	0.302785i	0.940097	−	0.340908i	$-0.110734\pi$
$971$	5.44733	+	9.43506i	0.174813	+	0.302785i	−0.765283	+	0.643694i	$0.777401\pi$
$972$	7.32941	−	13.7579i	0.235091	−	0.441285i
$973$	−27.2453	−	4.05184i	−0.873443	−	0.129896i
$974$	−7.51094	−	2.73376i	−0.240666	−	0.0875952i
$975$	0.681752	+	0.564179i	0.0218336	+	0.0180682i
$976$	2.49273	−	0.907280i	0.0797904	−	0.0290413i
$977$	−30.6407	−	25.7106i	−0.980284	−	0.822556i	0.00384822	−	0.999993i	$-0.498775\pi$
$977$	−30.6407	−	25.7106i	−0.980284	−	0.822556i	−0.984132	+	0.177437i	$0.943220\pi$
$978$	1.68215	+	2.86821i	0.0537892	+	0.0917153i
$979$	1.55880	−	1.30799i	0.0498196	−	0.0418036i
$980$	3.79508	+	16.3313i	0.121229	+	0.521685i
$981$	42.2390	−	36.4360i	1.34859	−	1.16331i
$982$	4.80688			0.153394
$983$	−43.3942	−	15.7942i	−1.38406	−	0.503756i	−0.460653	−	0.887580i	$-0.652385\pi$
$983$	−43.3942	−	15.7942i	−1.38406	−	0.503756i	−0.923406	+	0.383824i	$0.874607\pi$
$984$	16.5643	−	14.0928i	0.528052	−	0.449261i
$985$	−29.4994	−	24.7529i	−0.939929	−	0.788694i
$986$	30.9165	−	11.2527i	0.984581	−	0.358358i
$987$	−0.242095	−	7.17725i	−0.00770596	−	0.228455i
$988$	0.594220	+	3.36999i	0.0189047	+	0.107214i
$989$	7.85376			0.249735
$990$	0.909369	−	5.60319i	0.0289016	−	0.178081i
$991$	36.9889			1.17499			0.587495	−	0.809227i	$-0.300114\pi$
$991$	36.9889			1.17499			0.587495	+	0.809227i	$0.300114\pi$
$992$	−5.43257	−	1.97729i	−0.172484	−	0.0627791i
$993$	−0.495694	+	0.872252i	−0.0157304	+	0.0276801i
$994$	17.2394	−	3.52028i	0.546800	−	0.111657i
$995$	33.5750	+	28.1727i	1.06440	+	0.893136i
$996$	−1.59106	+	9.39774i	−0.0504148	+	0.297779i
$997$	18.6552	−	15.6536i	0.590815	−	0.495753i	−0.297663	−	0.954671i	$-0.596207\pi$
$997$	18.6552	−	15.6536i	0.590815	−	0.495753i	0.888479	+	0.458918i	$0.151763\pi$
$998$	17.5850	−	30.4580i	0.556642	−	0.964132i
$999$	4.71659	−	8.56965i	0.149226	−	0.271132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.a.193.6	✓	72
7.2	even	3		378.2.w.b.247.3	yes	72
27.7	even	9		378.2.w.b.277.3	yes	72
189.142	even	9	inner	378.2.v.a.331.6	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.193.6	✓	72	1.1	even	1	trivial
378.2.v.a.331.6	yes	72	189.142	even	9	inner
378.2.w.b.247.3	yes	72	7.2	even	3
378.2.w.b.277.3	yes	72	27.7	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.289127 + 1.70775i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.25076 - 0.819210i) q^{5} +(1.73201 - 0.0118132i) q^{6} +(2.25488 - 1.38402i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.83281 - 0.987512i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.289127 + 1.70775i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.25076 - 0.819210i) q^{5} +(1.73201 - 0.0118132i) q^{6} +(2.25488 - 1.38402i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.83281 - 0.987512i) q^{9} +(-1.19760 - 2.07431i) q^{10} +(-0.742338 - 0.270189i) q^{11} +(-0.312394 - 1.70365i) q^{12} +(0.651399 - 0.237090i) q^{13} +(-1.75455 - 1.98029i) q^{14} +(0.748249 + 4.08059i) q^{15} +(0.766044 - 0.642788i) q^{16} +(4.10222 + 7.10526i) q^{17} +(-0.480597 + 2.96125i) q^{18} +(2.46823 - 4.27510i) q^{19} +(-1.83484 + 1.53961i) q^{20} +(1.71161 + 4.25093i) q^{21} +(-0.137179 + 0.777978i) q^{22} +(0.428299 - 2.42900i) q^{23} +(-1.62352 + 0.603483i) q^{24} +(0.564595 - 0.473751i) q^{25} +(-0.346602 - 0.600332i) q^{26} +(2.50546 - 4.55221i) q^{27} +(-1.64553 + 2.07177i) q^{28} +(3.76826 + 1.37153i) q^{29} +(3.88866 - 1.44547i) q^{30} +(5.43257 - 1.97729i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(0.676045 - 1.18961i) q^{33} +(6.28497 - 5.27372i) q^{34} +(3.94139 - 4.96232i) q^{35} +(2.99972 - 0.0409212i) q^{36} +1.88252 q^{37} +(-4.63876 - 1.68837i) q^{38} +(0.216553 + 1.18097i) q^{39} +(1.83484 + 1.53961i) q^{40} +(-11.7991 + 4.29451i) q^{41} +(3.88913 - 2.42377i) q^{42} +(0.552932 + 3.13583i) q^{43} +0.789980 q^{44} +(-7.18496 + 0.0980148i) q^{45} -2.46647 q^{46} +(-1.47259 - 0.535978i) q^{47} +(0.876236 + 1.49406i) q^{48} +(3.16898 - 6.24160i) q^{49} +(-0.564595 - 0.473751i) q^{50} +(-13.3201 + 4.95125i) q^{51} +(-0.531025 + 0.445583i) q^{52} +(-4.62037 + 8.00272i) q^{53} +(-4.91812 - 1.67692i) q^{54} -1.89217 q^{55} +(2.32604 + 1.26077i) q^{56} +(6.58717 + 5.45117i) q^{57} +(0.696346 - 3.94917i) q^{58} +(-9.91385 - 8.31871i) q^{59} +(-2.09877 - 3.57858i) q^{60} +(2.49273 + 0.907280i) q^{61} +(-2.89061 - 5.00668i) q^{62} +(-7.75439 + 1.69395i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.27192 - 1.06726i) q^{65} +(-1.28893 - 0.459201i) q^{66} +(0.213835 - 1.21272i) q^{67} +(-6.28497 - 5.27372i) q^{68} +(4.02429 + 1.43372i) q^{69} +(-5.57134 - 3.01982i) q^{70} +(-3.32517 + 5.75936i) q^{71} +(-0.561196 - 2.94704i) q^{72} -7.17241 q^{73} +(-0.326897 - 1.85392i) q^{74} +(0.645809 + 1.10116i) q^{75} +(-0.857208 + 4.86147i) q^{76} +(-2.04783 + 0.418167i) q^{77} +(1.12543 - 0.418337i) q^{78} +(-1.70323 - 9.65951i) q^{79} +(1.19760 - 2.07431i) q^{80} +(7.04964 + 5.59487i) q^{81} +(6.27815 + 10.8741i) q^{82} +(-5.17113 - 1.88214i) q^{83} +(-3.06229 - 3.40916i) q^{84} +(15.0538 + 12.6317i) q^{85} +(2.99218 - 1.08906i) q^{86} +(-3.43174 + 6.03869i) q^{87} +(-0.137179 - 0.777978i) q^{88} +(-1.28793 + 2.23076i) q^{89} +(1.34418 + 7.05878i) q^{90} +(1.14069 - 1.43616i) q^{91} +(0.428299 + 2.42900i) q^{92} +(1.80602 + 9.84915i) q^{93} +(-0.272123 + 1.54329i) q^{94} +(2.05319 - 11.6442i) q^{95} +(1.31920 - 1.12236i) q^{96} +(-2.83825 - 16.0965i) q^{97} +(-6.69706 - 2.03699i) q^{98} +(1.83609 + 1.49846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Introduction

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